The value of $\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}(x^5+x^3+x+2)dx$ is :

0 2 $2\pi $ $\pi$

$2\pi $

The correct answer is Option (3) → $2\pi $ $I=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}(x^5+x^3+x+2)dx$ $⇒I=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}2dx=2(\pi)$ $=2\pi $