Now you will all point at me and laugh. I tried to prove that $\displaystyle \int_{0}^{\pi}\sin^{3}\theta d\theta=\frac{4}{3}$ and all I get is

$\displaystyle \int_{0}^{\pi}\sin^{3}\theta d\theta=\left[3\sin^{2}\theta\cos\theta\right]_{0}^{\pi}=3*0^{2}*(-1)-3*0^{2}*1=0$

Where does it all go so wrong?