Hey guys i kind of have a weird little problem which i can't figure out.

I'm integrating sinxcosx, and depending on what i use as my substution you get two answers.

1) sin^2x/2 + C and 2) -cos^2x/2 + C

Now if we set these two answers equal to eachother we get

sin^2x + cos^2x = 0 but we know there exists a trig identity that states sin^2x + cos^2x = 1

So i'm confused here. How can this be possible? I know that 0 cannot equal 1. Or at least i hope not hehe. Any help would be great cheers