Hi, I was doing a question with this simple integral

so rather than do it by parts (which probably would turn out to be double back on itself so you get the integral again), I opted for using sin2x = 2sinxcosx

so that means the integral simplified to

which integrates to

so wack in the limits and I get 3a[1-1] = 0

but that isn't right is it?

The answer scheme suggest =

but i) How come my method doesn't work

ii) How can the mark scheme do that. You can't just do that!?

Thanks