How To Integrate sin^2(x)

 

\begin{array}{l} \smallint {\sin ^2}xdx\\\\ \smallint \frac{{1 - \cos 2x}}{2}{\rm{d}}x\\ \smallint \frac{1}{2}\frac{{ - \cos 2x}}{2}{\rm{d}}x\\ \Rightarrow \frac{1}{2}x - \frac{{\sin 2x}}{{2 \cdot \left( 2 \right)}} + c \end{array}