Historians generally are also historicists, which is to say, we are usually advocates of historicism, which is the belief/ideology that everything and everyone is shaped by its historical context. This is one of the reasons to be a historian — to understand historical context is to understand how the world works. (As opposed to being an economist, who foolishly think that markets run everything. Ha!)

But it also means that we would have to be dishonest or hypocritical to think that we are somehow above this. After all, everything and everyone in the above doesn't carry a magic caveat that says "*except historians." Now, arguably, maybe as people who study historical context, we can be meta-aware of it — we can see it coming, we can see how it influences us better than the average person, we can better understand ourselves as we attempt to understand our historical context, and maybe that can make us what we call reflexive. "Reflexivity" (one of my least favorite words but a rare example of useful jargon) means applying one's theories/analysis backwards on one's self, and is not limited to the study of history (anthropologists, for example, are big on reflexivity — you cannot study another culture well if you do not recognize that your culture is not a special, "neutral" culture, but yet another possible specimen for anthropological analysis). A reflexive historian will say, "ah, I am a product of history myself, and this necessarily shapes the history I produce!"

If you are a real historicist, there is no way out of the bind. There is no way to not be a product of your historical culture. However, being aware of it, being careful about it, and striving for one's best anyway, these are always available options. Any good historian has no doubt that in 50 years, historians will (if they are still reading one's work!) laugh about how dated it is, and how of its time it was, and so on. That is fine; we should not expect the future to treat us any more kindly than we do the past!

In my own work, it is hard not to feel how much my own historical context shapes what kinds of questions I am interested in. The "previous generation" of work on the history of nuclear weapons was the one that saw the end of the Cold War. A huge number of the book written in the 1990s were along the lines of "the Cold War was avoidable, it was the product of fear and paranoia, etc."

When I teach, I tell my students to pay attention to the birth dates of historical actors not because they are interesting in and of themselves, but because if you add 20 to them you can tell when they "came of age" and that often tells you quite a lot. Someone born in 1921, well, who cares? Ah, but they came of age in 1941 — World War II — and that probably affected them quite a bit and tells you a lot about which "generation" they were.

If you apply the same math to myself you find I came of age in the early 2000s, and was fully sentient (and "adult") at the time of the 9/11 attacks, the War on Terror, the Iraq War, etc. For this reason, perhaps, I am less willing to claim (as the generation before me is) that the Cold War, etc., was just a big farce — I tend to see the world as a pretty unpleasant and dangerous place, and definitely don't see a stark line dividing the Cold War from the present period of history. (To be fair, since the 2000s I suspect those historians that wrote the books of the 1990s don't quite see things as cleanly as they did then, either.)

Does this mean that everything I write is devoid of fact and value? Of course not — at least, I don't think so! Does it affect the kinds of questions I ask, the kinds of analysis I find plausible, the kinds of narratives I tend to write? Without a doubt. Will someone in the future find these less resonant and important with their historical context? One can only hope!

For my dissertation, I'm writing a meta-biography of a mathematician....hence, I've started to become more and more aware of this problem. As you said already, the intention of the individual author will have a huge influence. The way you phrase it, the intention of the author is something that is known to him, as he has a certain idea of what impact their work should have. Hence, it is possible that the accounts of different historians of the same subject may differ significantly. This undoubtely true, as each source is open to interpretation. Let me give you a very drastic example for this:

As you know, we have leap years to make up for the fact that the length of the year is really a little bit more than 365 days. This was also known in the past hence the introduction of leap years by Julius Ceasar. As a result, the Julianian year has a length of 365,25 days. Unfortunately, the tropical year is slightly shorter (this is the reason we nowadays don't have leap years in the years that can be divided by 400) and this mistake adds up to a full day in 128 years. Hence, in 1582 Pope Gregory XIII decided to strike 10 days in order to rectify the calendar. As can be shown by some easy arithmetics, the summed up mistake had in fact by then become 13 days, not 10. Still, the calendar was correct afterwards.

There are many valid explanations for this, mostly of astronomical nature. A German scholar named Heribert Illig, on the other hand, came up with a different one: In his opinion, about 300 years (equalling 3 days of "mistake") didn't happen. He believes that everything between 614 and 911 AD is just made up and that Emperor Otto II and Pope Sylvester II fabricated a new dating system in order to reign at the turn of the millenium. In order to stress this rather bold thesis, he interprets the sources stemming from this period quite differently than (I'm gonna say) serious scholars do, all in all as frauds manufactured by later generations. This is a very striking example of how certain beliefs and intentions shape a historians view on sources. (I would like to add that I believe that Illig is a complete nutbag, but he is a very good example for this argument).

But next to this very contious influences on the way history is written, it is important to remember the many factors that subcontiously flow into and determine the outcome of each individuals research. Each book and article is also influenced by the nationality, gender, religion, personal beliefs, social enviroment, upbringing, education... of the respective author. (And even if you are aware of this, you're personal beliefs will flow into your use of a source, more or less subconciously.) Let me give you an example stemming from my work:

The mathematician I work on, once claimed, that all her work was done in the spirit of another mathematician (let's call him "W"). Hereby, she wanted to stress her affiliation to a certain circle of mathematicians, who were called a school and had some basic ideas going back to "W" that can be found (to a certain extent) in each's work. In a biography, written by a friend of hers, the author rephrased this quotation in words that say that all her work consisted of ideas of "W". While I believe, the author wanted to say exactly what the mathematician had expressed, from then on, many "historians"* wrote, that she only executed ideas of "W" (refering to the biography of the friend), thereby diminishing her work.

The reasons for this were manifold: Many took the friend's words as a given, as they were influenced by their belief that women weren't creative mathematicians and could only execute mathematical tasks given to them -- this is connected to certain ideas of the sexes prevalent at the time in Germany. They were brought up in this belief system and believed it to be true, very likely very unconcious to the fact, that those values determined their outlook on this quotation. At least some of them had the knowledge to look at the work of the mathematician and --had they done so -- would have had realized, that she was a very independent mathematician. They didn't, because they didn't feel the need to, as the quotation was in accord what they believed to be true.

Most of them were men and they were also influenced by their gender: By drawing on this quotation in oder to stress their opinion that women shouldn't be allowed to go to university (which most of them did), they tried to secure a certain hegemonic dominance of the male sex. The women who brought up this quotation (some of them also to make their point that women in general were unfit for academic careers), also did this to undermine certain predujudices of the female sex they had; mostly that women could only be happy as wifes and mothers and were biologicaly unfit for academic careers.

Others citing the friend's biography in this context believed that the mathematician belonged to a certain circle of mathematicians who didn't work autonomously enough and drew on the quotation as a proof for this. Here again, her work was not consulted for a check, as in their eyes the quotation was proof enough for something they considered a given to begin with.

In short, there is no such thing as "neutral history": The historians personal background always influences the content of a source, or more precisely, what you consider the context of a source to be -- this happens conciously as well as unconciously. While everyone is aware that sources are tendentious and should be read in this spirit, you should also aware that historical literature is a source as well and you should always treat it as such.

*I Don't want to start a discussion who counts as a historian and who doesn't.....

I think my context has a huge effect on what kind of questions I find interesting. I studied modern Ireland. Traditional Irish history was largely about how Ireland became independent. As someone who is from a mixed nationality and is not a nationalist politically, I wasn't interested in this. I was more concerned with state power as expressed in censorship or welfare. It's no coincidence that I grew up watching the Northern Ireland troubles and was very alienated by nationalism. I also grew up in a country that was liberalising rapidly both economically and morally so I wanted to know how it had got that way.