How important is trust?

I don't trust my bf I can tell you that for free and I think that's probably our biggest problem because I let stuff get to me that with any other guy wudn't bother me at all. Then we fall out and he tries to make everything ok again, the problem is I'm still not ok and it only take one other little thing to come along and screw things up again.

The worst part is I don't think I can ever gain that trust for him. The thing is when he was with his last gf he text me and flirted with me to say the least, but now I'm the gf I wanna know who the girl he flirts with is.

Lately I'm starting to think he's been having "conversations" with this girl, I don't know what to do. I feel that if I confront him about it, it'll be the end of us but if I leave it alone it's just gonna play on my mind.