How do you integrate [sin(2Pi*x)/L)][sinPi*x)/L)] with limits of L and 0

∫(x = 0 to L) sin(2πx/L) sin(2πx/L) dx
= ∫(x = 0 to L) sin^2(2πx/L) dx
= ∫(x = 0 to L) (1/2)(1 - cos(4πx/L)) dx
= (1/2)(x - (L/(4π)) sin(4πx/L)) {for x = 0 to L}
= L/2.

I hope this helps!