Would you admit to previously cheating in a past relationship?

Recently I started a relationship with a guy, who has the same long-term views as me. We are looking (and hoping) to do long-term (think marriage). My ex partner is still part of my life as we share custody of our kids. Little background, on my ex and I; he was/is a very abusive person towards me. Our relationship lasted 10+ years, in which hitting me and creating a environment of pure hostility was the norm. I constantly feared for my life and several police reports were made. During my hell I made a long distance relationship that lasted 5 years. It was very emotional and we only got the chance to meet once. I am forever grateful for him as he saved me from the falling of into depression and suicidal thoughts.
Anyways, our separation was due to a variety of things and the fact that I had grown deep resentment and hate for him due to years of abuse.

I want to start clean with my current partner, and I do admit I am somewhat paranoid this may come out later on. I dont want him to feel I am hiding something. My communication with my LD "friend" ended and I eliminated all his contact info.
Another part of me also feels, the past is the past. What do you think?
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Would you admit to previously cheating in a past relationship?
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