How do I tell them??

So last year in November, my ex boyfriend and I BOTH made a really dumb decision to get intimate at my house and my dad came home and caught us early on in the act. We (mostly me) caught hell from the situation and my parents, I was 19 at the time and he was 21. After that we cooled off for a bit and took some space also outta respect for my parents. We rekindled in January and have been building to start dating again, my parents know that we have still been talking as I’ve told them that but they don’t know that we’ve been hanging often since January. We’ve all moved past the incident and he’s definitely apologized to my dad and it’s something that will NEVER happen again but we both want to be together but I’m hesitant bc of idk what my parents will think. They can be pretty controlling and I don’t want them to shut it down bc of past mistakes BUT I also don’t want to keep being dishonest about me hanging with him, I am 20 years old and I can see how it’s really none of their business but I do live under their household. What should I do??