Heartbroken but with hope

I recently found out that my boyfriend of 10 months has been sexting a girl on and off for a few months and recently stopped. He says he stopped because he realised that I was the one for him and our relationship the past month has been better than ever before. I never imagined that he would do something like this to me, i trusted him completely. When he told me i was devastated and so was he, i have honestly never seen him so remorseful and desperate to make me happy again, i cant let him go and we talked it through and are trying to get back on track. However, i now have some serious trust issues and i cant stop thinking about it and what those sexts said. Am i right to go with my heart on this and try to rebuild what we have or is there no hope...? Any experiences might help.