The range of the function $f\left(x\right)=\frac{\tan \left(\pi \left[x+1\right]\right)}{x^4+1}$ (where, $\left[·\right]$ is the greatest integer function) is

• A

  $\left[0,1\right]$
• B

  $\left[-1,1\right]$
• Correct answer
  C

  $\left\{0\right\}$
• D

  $\left(-\infty ,\infty \right)$

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