About five months ago, I opened my boyfriend's computer and his facebook message inbox was open...?

I saw a name of a girl that had commented on his profile picture a few times so I became curious. So I read the messages between them and immediately felt sick. He said "bed me." to her in one of them and he flirted with her in a few other messages. I had snooped on him once before and it had nearly broken his heart that he couldn't trust me... So I decided that it was probably nothing and that I shouldn't talk to him about it for a while. That was on New Year's Eve. Now it is nearly six months later and I feel so much for him but I am not sure if he has stayed faithful to me (we have been together about a year in total.) I think a lot about coming clean about invading his privacy but I am worried I will lose him. I am also worried what he will tell me. I know that they are still in contact. I have even tried asking him about her in a roundabout way but he has assured me that he's not attracted to her in that way and that he has never cheated on me. I want so much to believe him but I also do not want to be living a lie...