JEE Math Practice Question

Let f : R $$\to$$ R be a continuous function. Then $$\mathop {\lim }\limits_{x \to {\pi \over 4}} {{{\pi \over 4}\int\limits_2^{{{\sec }^2}x} {f(x)\,dx} } \over {{x^2} - {{{\pi ^2}} \over {16}}}}$$ is equal to :

1. A.f (2)
2. B.2f (2)
3. C.2f $$\left( {\sqrt 2 } \right)$$
4. D.4f (2)