If $\int \frac{d x}{(x \tan x+1)^2}=f(x)+c$, then $\lim _{x \rightarrow \frac{\pi}{2}} f(x)=$

• A

  $\frac{\pi}{2}$
• Correct answer
  B

  $\frac{2}{\pi}$
• C

  $\frac{1}{\pi}$
• D

  $\infty$

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