I'm not really sure what to say but all of the above comments give very good advice. Personally I think that if the affair happened before you got together then maybe you should give him a chance. Are the text messages that you found old ones that he had kept on his phone? if they are then there are 2 ways to look at that, in one way it's good that they aren't recent but in another way why would he keep the texts if he isn't bothered about the other woman?
Whatever you decide I hope that it is the right decision and that everything works out ok for you