Can a marriage be successful even with a past history of cheating when you're boyfriend and girlfriend?

I'm worried for my female cousin. She's currently engaged for 6 months but the guy cheated on her 5 years ago. He was her boyfriend at the time. I still remembered that day like yesterday.

She visited me and was crying. He came clean the next day and told her the truth. She broke up, he went to counseling and they got back together like about 6 months later or so. They worked things out and we're engaged by now. Personally I would never accept a marriage proposal from someone that cheated on me when I was a girlfriend, much less marry him. I still don't like the guy for what he did to her but have to be cordial when he's around.

Can a relationship really survived cheating to the point, it isn't just reconciliation but they still get married? Married with a past cheating when you were just boyfriend and girlfriend.

Can a marriage be successful even with a past history of cheating when you're boyfriend and girlfriend?
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