$$\lim_{x \rightarrow \frac{\pi}{4}}\frac{\int_{2}^{\sec^2 x}f(t)dt }{x^2 - \frac{\pi^2}{16}}$$ equals

A

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

B

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

C

$$\frac{2}{\pi}f\left(\frac{1}{2}\right)$$

D

$$4f(2)$$