Answer
$${\text{si}}{{\text{n}}^2}x = \frac{{1 - \cos 2x}}{2}$$
Work Step by Step
$$\eqalign{
& \int {{{\sin }^2}x} dx \cr
& {\text{We need to use the identity si}}{{\text{n}}^2}x = \frac{{1 - \cos 2x}}{2} \cr
& \int {{{\sin }^2}x} dx = \int {\frac{{1 - \cos 2x}}{2}} dx \cr
& {\text{Separate the integrand}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \int {\frac{1}{2}} dx - \int {\frac{1}{2}\cos 2x} dx \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{2}x - \frac{1}{4}\sin 2x + C \cr} $$
