Suppose $f:[0, \pi] \rightarrow \mathbb{R}$ satisfies $f(x)+f(\pi-x)=1$ for all $x$. Then $\int_0^\pi f(x) \sin x d x$ is

• A

  $1 / 4$
• B

  $1 / 2$
• C

  $3 / 4$
• Correct answer
  D

  $1$

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