Given that $\displaystyle \frac{1}{2} \le \sin^{2}(x) \le 1$ on $\displaystyle \left[\frac{\pi}{4}, \frac{3\pi}{4}\right]$ to estimate $\displaystyle \int_{\pi/4}^{\,3\pi/4} {\sin^{2}(x)}\, dx\,.$

$\displaystyle \le \int_{\pi/4}^{\,3\pi/4} {\sin^{2}(x)}\, dx \le$