If $$f(x) = \int\left(\frac{x^2 + \sin^2 x}{1+x^2}\right)\sec^2 x\,dx$$ and $$f(0) = 0$$, then $$f(1)$$ equals

A

$$\tan 1 - \frac{\pi}{4}$$

B

$$\tan 1 + 1$$

C

$$\frac{\pi}{4}$$

D

$$1 - \frac{\pi}{4}$$