The first day of my last period was April 11, 2010. Me and my boyfriend had sex on April 17th and broke up. I had sex with my new boyfriend on April 24th and 25th. What was my conception date I need to be 100% positive.

You cannot be 100% certain on these dates, or even close.
The ONLY sure way to ascertain who the father is would be a DNA test once the child is born.
That is of course assuming you are indeed pregnant.