By using the properties of definite integrals,evaluate the integral $\begin{align*}\int\limits_\frac{\Large -\pi}{\Large 2}^\frac{\Large \pi}{\Large 2}\sin^2\;x\;dx \end{align*}$

Question

$\begin{array}{1 1} \frac{\pi}{2} \\ \frac{\pi}{4} \\ \frac{\pi}{16}\\ \frac{\pi}{8} \end{array} $