$\displaystyle \displaystyle\lim_{x\to \pi/4} \left(\frac{\int_{2}^{sec^2 x} \left(f(t) dt) \right}{x^2 - \frac{\pi^2}{16}}\right) $ equals

(A)$\displaystyle \frac{8}{\pi} f(2)$

(B)$\displaystyle \frac{2}{\pi} f(2)$

(C)$\displaystyle \frac{8}{\pi} f(\frac{1}{2})$

(D)$\displaystyle 4f(2)$