$\int_0^\pi \frac{x \sin x}{1+\cos ^2 x} d x=$

• Correct answer
  A

  $\frac{\pi^2}{4}$
• B

  $\frac{\pi}{2}$
• C

  $\frac{\pi^2}{2}$
• D

  $\frac{\pi}{4}$

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