The integral $\mathrm{{\rm I}}=\int e^x\left(\frac{1+\sin x}{1+\cos x}\right)dx=e^{x}f\left(x\right)+C$ (where, $C$ is the constant of integration). Then, the range of $y=f\left(x\right)$ (for all $x$ in the domain of $f\left(x\right)$) is

• A

  $\left[-\mathrm{1,1}\right]$
• Correct answer
  B

  $\left(-\mathrm{\infty },\mathrm{\infty }\right)$
• C

  $\left(-\mathrm{1,1}\right)$
• D

  $\left[0,\mathrm{\infty }\right)$

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