Let $I(R)=\int_0^R e^{-R \sin x} d x, R\gt0$. then,

• A

  $\quad \mathrm{l}(\mathrm{R})\gt\frac{\pi}{2 \mathrm{R}}\left(1-\mathrm{e}^{-\mathrm{R}}\right)$
• B

  $\quad$ I $(\mathrm{R}) \lt \frac{\pi}{2 R}\left(1-\mathrm{e}^{-\mathrm{R}}\right)$
• C

  $\quad \mathrm{I}(\mathrm{R})=\frac{\pi}{2 \mathrm{R}}\left(1-\mathrm{e}^{-\mathrm{R}}\right)$
• Correct answer
  D

  I(R) and $\frac{\pi}{2 R}\left(1-e^{-R}\right)$ are not comparable

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