JEE Math Practice Question

The value of $$\int\limits_{ - \pi /2}^{\pi /2} {{{dx} \over {\left[ x \right] + \left[ {\sin x} \right] + 4}}} ,$$ where [t] denotes the greatest integer less than or equal to t, is

1. A.$${1 \over {12}}\left( {7\pi - 5} \right)$$
2. B.$${1 \over {12}}\left( {7\pi + 5} \right)$$
3. C.$${3 \over {10}}\left( {4\pi - 3} \right)$$
4. D.$${3 \over {20}}\left( {4\pi - 3} \right)$$