How do I integrate sin^2 (x) dx?

The key to answering this question is to recognise that a common substitution of u=sin(x) wont work straight away so we must write the integral in a different form. Knowing that cos(2x)=1-2sin^2(x), the sin^2(x)=(1/2)(1-cos(2x)). Therefore the integral equals the integral of (1/2)(1-cos(2x)). We know the integral of cos(2x) dx is (1/2)*(sin(2x)). Thus the integral of sin^2(x)dx equals (x-(1/2)*sin(2x))/2.