If $f\left(x\right)$ is a non-negative function such that the area bounded by $y=f\left(x\right),$ $x$-axis and the lines $x=0$ and $x=\alpha$ is $4\alpha \sin \alpha +2$ sq. units $\left(\forall \alpha \in \left[0,\pi \right]\right),$ then the value of $f\left(\frac{\pi }{2}\right)$ is equal to

• A

  $0$
• Correct answer
  B

  $4$
• C

  $2\pi$
• D

  $8\pi$

Hence, the correct answer is option: 'B'.