Has anyone ever been cheated on and worked it out?

I had been single my whole life until my boyfriend and never understood how someone could stay in a relationship after being treated poorly.

Essentially I read my bf’s journal while he was out getting us food. [it was out in the open and he’s read me things from it before, so I didnt think he had anything to hide]. He wrote that he had made a ‘mistake’ with a girl I know he had been close with and someone had told me they were getting touchy while I wasn’t around. I go to school an hour away so we don’t always see each other often, and at that point in time our relationship wasn’t official. Now I am home for the summer and things seemed to be going well. But this journal entry was dated after we had begun dating, about 2 months ago. He wrote that he really respected me and wanted to do better and didn’t want to hurt me.

At the time I didn’t bring it up bc he seemed regretful and I have never suspected him of cheating other times. But now I can’t stop thinking about it. When it comes down to it I don’t want to be without him but I’m not sure I can be with him and feeling like trash that he would possibly do something. I don’t even know if ‘mistake’ means he slept with someone else. I think I could forgive if it was just a kiss or it just feelings. I’m not sure how to bring it up...

I know this was long but if you have any advice or have been in a similar situation I would really appreciate it.