Let $$f : \mathbf{R} \to \mathbf{R}$$ be a differentiable function such that $$f\left(\frac{\pi}{4}\right) = \sqrt{2}$$, $$f\left(\frac{\pi}{2}\right) = 0$$ and $$f'\left(\frac{\pi}{2}\right) = 1$$ and let $$g(x) = \int_x^{\pi} (f'(t) \sec t + \tan t \sec t \, f(t)) dt$$ for $$x \in \left[\frac{\pi}{4}, \frac{\pi}{2}\right)$$. Then $$\lim_{x \to \left(\frac{\pi}{2}\right)^-} g(x)$$ is equal to

A

2

B

3

C

4

D

$$-3$$