Answer
The Trigonometric Identity $sin^2(x) dx = \frac{1-cos(2x)}{2}$ would be useful.
Work Step by Step
Using $sin^2(x)$ = $\frac{1-cos(2x)}{2}$, $\int sin^2(x) dx = \int \frac{1-cos(2x)}{2} dx$.
This can be rewritten to be $\frac{1}{2} \int 1-cos(2x) dx$, which is easier to integrate.