I am studying for my final and I have come across two questions from an old exam that I can not figure out. Thanks to anyone who is willing to lend an ear!

integral of f(x) dx + 2 equals integral of f(x) dx + 6 both from 2 to 5

I am forgetting how to figure this out.

integral of sin^2 t dt I have tried by substitution, by parts with no luck

the answer on test is 1/2 integral of (1 - cos(2t)) dt How do you know this??????

Thanks again, I LOVE and APPRECIATE this site more than I can say!