JEE Math Practice Question

The value of the definite integral $$\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {{{dx} \over {(1 + {e^{x\cos x}})({{\sin }^4}x + {{\cos }^4}x)}}} $$ is equal to :

1. A.$$ - {\pi \over 2}$$
2. B.$${\pi \over {2\sqrt 2 }}$$
3. C.$$ - {\pi \over 4}$$
4. D.$${\pi \over {\sqrt 2 }}$$