Do you always have to use u-substitution? i.e. sometimes will you get a different answer to if you didn't? Im asking because I had the integral ∫sinxcosx dx between 0 and π/2 and the answer was 1/2 but I got 0. ∫sinxcosx dx between 0 and π/2=-cos(π/2)sin(π/2)=0 according to my calculations. What am I doing wrong? I don't thin this counts as homework style as I am hoping just to find out whether you always have to use u-substitution in certain case using the above question as proof.