What do you mean with "believe"? And what with "historical literature"?

Literature, by most definitions of the term, would imply fictionality, since we are speaking about texts with a primarily aesthetic function, which are typically either partially or entirely "made-up" (e.g., poetry, tales, novels, etc.).

Old texts that are not obviously of a primarily literary quality broadly fall into two categories: documents and records. The former serve to document acts that actually took place: the issuance of laws, appointments to office, bequests of property, etc. The latter serve to record events in the form of chronicles, diaries, and similar forms, and are clearly shaped by authorial and other forms of intent. They, too, claim to record the truth of the matter, but are always, to some degree, distorted through both human subjectivity and the conventions of genre. (This applies to documents, as well, although to a much smaller extent.) But moreover, even what clearly is a work of fiction (tales, novels, etc.) may contain truths of two kinds: specific truths, as in referencing events that actually happened, and general truths, as in telling us something about how people in the past generally saw the world or lived their lives.

We use source criticism to try and assert the trustworthiness of a text, no matter into which category it falls.

There is external source criticism, which examines the features of a text: its material properties such as the ink used, the paper (or other material) it is written in, the choice of words (does the style match the time it was allegedly created in), etc. This is usually done to ask of texts, "is this text authentic or a forgery?" There usually is not much to doubt about a document telling us of a sale of property when it is ascertained to be authentic—as long as it does not contradict other documents! —but much to doubt about it if it is a forgery. (But even if it is a forgery, it may be one made merely to replace an original that fell victim to the flames.)

There also is internal source criticism, which asks questions such as, "who was the author?", "for what purpose was the text written?", "in which kind of tradition of writing does this text stand?", "how does what this text claim compare to other texts that refer to the same events?", in order to assess the inherent biases of both an institutional and individual nature. We need this to assess where to have faith in a text, and to what extent—it is never just a question of believe or not believe, but a sliding scale of degree—and where to doubt whatever it tries to convince us of. But these inevitable biases do not necessarily imply the malicious intent of falsification: after all, the human memory is a fickle thing. And if I write down my own take on things, I write down my view of a matter, not the view of someone else. If I record things in my diary, I might only write down hearsay: how can I know how accurate the stories are they tell each other in the streets about things that happened hundreds of miles away? And if I compile a chronicle a hundred years after the fact, I am restrained by the materials I have available at the time (and, certainly, by the demands the form of the genre imposes on me).

We may trust whatever remains of a text after it has been exposed to criticism, but only to the extent, the degree of certainty, that can be rationally justified.