I am an early medieval historian (600-900 in Western Europe), and this is a really important concern for historians in my field. This issue is especially troubling for the Carolingian period, because the only sources we have that talk about Peppin the Short's ascension to the Frankish throne in 751 were written decades later with a specifically Carolingian rather than Merovingian perspective. According to 9th century writers, the Merovingian dynasty was decaying, the government failing, and the church corrupt. However, some historians, like Constance Bouchard in Rewriting Saints and Ancestors, have argued that these 9th century Carolingian writings were an attempt by later authors to legitimize Carolingian usurpation of the Frankish throne.

The issue of perspective in history and the recognition that the text that survives is not an "authentic" representation of the past has been a central focus of historiography (the study of the study of history) for the past several decades. Beginning in the 1980s, the Linguistic Turn put a new emphasis on the language of the texts, that is the "discourse" evoked by texts, in order to understand how one author viewed the past. Historians do not assume that the text presents a reality. Rather, historians must recognize that the text can only tell us about the text itself. The Linguistic Turn has changed the way historians talk about history. It's no longer the study of what happened, but it's the study of what people say happened. It's a subtle shift, but it's been crucial to shaping the field over the last several years.

History by its very definition is biased. The presentation of facts of when a battle occurred and how many people died is not really History in the academic sense. There are varying perspectives not only in the primary sources, but also in the works of modern historians.

One particularly useful way that early medieval historians have begun to resolve these issues is through the lens of memory studies. Constance Bouchard's Rewriting Saints and Ancestors and James Palmer's Anglo-Saxons in the Frankish World are two excellent examples of this trend. Rather than looking specifically at what a source like a biography of a saint tells us about the saint (who may have died 100 years earlier), scholars using memory studies are looking to see how later authors are actively rewriting the past to suit their present needs and concerns. By looking at a source like the Vita Leobae (a 9th century biography of an 8th century female saint), we can understand how the 9th century authors re-wrote the memory of Leona to fit present concerns over monastic reform. The idea here is that although the text fails to be a reliable tool to learn about the saint herself, we can use the source to learn about the time period it was written during.

Overall, the goal of historians today is to find the differences and similarities between sources and identify /why/ those differences/similarities may exist. It requires being aware of a large repertoire of sources that you can read against one another. There isn't really a recoverable "true" history, but we can use these texts to tell us how people in the past talked about and considered their lives.

Other answers are always welcome, but you may find this section of the FAQ has a wealth of answers on this exact topic.

I think this was answered before but I did want to jump in with an additional question: How do historians account for first person bias/culture at that time bias (such as diaries), especially if there are no tertiary stories to corroborate?