Cheating? Flirting? Leave? Or stay?

So my boyfriend and I have known each other for a little more than a year and been in a relationship since End of May early June.. Anyways.. I've never had that doubt to have to question him cheating or anything. You know usually ladies we have that "gut feeling" well wasn't feeling everything.. Actually thought we were good. Yesterday morning I woke up out of my sleep and something just told me to go through his old phone.. He ended up leaving to the store and left his old phone on the dresser.. I went into the room and seen the phone.. Told myself not to do it multiple times but of course I gave in and went through it. Him and a female at his job have been texting... Not as if their friends but very flirtatious.. And this was the first time of seeing anything like this.. I've spoke to a few friends to see their opinions.. See if they say stay and give him a chance or leave.. He apologized said he was wrong and he didn't want to lose me.. I met his parents on thanksgiving.. For the first time and everyone made it a big deal because he never brings a female to his parents house... I'm kinda torn.. And trust is very iffy now... 2 of my friends and Dad said lets see how he proves hisself and see if he shows he won't do it again and try to gain his trust... One friend say leave him... Opinions?....