Should I break up with my girlfriend? I found text messages from her ex.

My on again/off again gf of 2 years is back in touch with her ex. She basically has gone between us for a long time. She and I have had an exclusive relationship for the past 3 months. I got suspicious of her over the weekend because when we went out, she would text on her phone. I repeatedly asked her not to because it was rude. Anyway, I had an opportunity to check her phone last night and saw that she was texting her ex for at least four days (probably longer). They weren't sexual texts, but it was clear that she never told him that she was dating me. In fact, she wrote to him that he should delete his texts so his gf wouldn't find them. She promised that she cut off all contact with him months ago. Now, of course, I don't trust her anymore. So, i want to know how I should breakup with her without revealing that I checked her messages. Or, maybe I should reveal that I checked her messages... not sure. I feel embarassed taht I had to spy on her.