When you say trust, you mean that they are faithful and won't cheat on you, then no, I wouldn't say that I would trust someone with that kind of a history. If they are notorious for cheating a lot, they'll most likely have affairs no matter what. To them, cheating has become somewhat of a habit and old habits die hard. Nobody can change their habits in a matter of weeks or months or sometimes even years. Some people can never change out of their habits. Why do you think they were notorious about having affairs in the first place?
I know that in movies and in romance novels they depict a player as someone who's just lost and confuse and will eventually stop when they find their true love. Don't get me wrong, there are people who do have this sort of story, but for most that is just pure fiction. That's why no matter how much this person says that they have changed or whatever, I wouldn't trust them. But if you feel like they should be given a chance, then that's up to you. I just personally wouldn't. And if you do give them a chance, just be careful and be prepared to find out if they were having an affair.