Evaluate $\int \sin^{2} x\,dx$.

Explanation

1. 01

   Rewrite first: $\sin^2 x = \frac{1 - \cos 2x}{2}$.

2. 02

   Then each term is standard: $\frac{x}{2} - \frac{\sin 2x}{4} + C$.

3. 03

   Check: differentiating the answer gives back the integrand.