$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin (x-[x]) d x=$

• A

  $0$
• Correct answer
  B

  $3(1-\cos 1)+\sin 2-\sin 1$
• C

  $3(1-\cos 1)+\cos 2-\sin 1$
• D

  $\cos 2-\sin 2$

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