So long as they use textbooks which are not full of Creationism or religious rhetoric, yes, I think anthropology professors do a good job of explaining human history. There is much we do not know yet, and also much which is pure speculation, but what facts we do know are well-presented in most modern-day textbooks and the teachers do a good job of helping students to understand those textbooks.
I believe that anthropology professors do a good job of explaining human history. Since we don't have all of the information, its hard to say if its 100% accurate and often they will have new findings, but explain that it needs to be further backed up by more evidence. I think the field has unearthed many new findings over the years and the professors certainly have a lot to keep up with.
Anthropology professors do a good job of explaining human origins, not necessarily human history. Anthropologists are more concerned with human beings up to the point of civilization starting several thousand years ago. Once human writing systems start, historians take over to explain human existence. Anthropologists can only go so far in prehistory.
Yes, I think that anthropology professors do a good job of explaining human history accurately, because they rely on facts and objective evidence that they have learned through their work. They use this information to provide clues as to how people lived many years ago. Anthropologists rely on evidence, and are thus, accurate at explaining history.
Unfortunately, many anthropology professors do a terrible job of explaining human history accurately, according to their field. The fact of the matter is that anthropology is not that sound as far as evidence is concerned. It's a fringe subject that many people have questioned and will continue to question today.