The functions f and g are given by $f\left(x\right)=\left\{x\right\}$ the fractional part of $x$ and $g\left(x\right)=\frac{1}{2}\sin \left[x\right]\pi ,$ where $\left[x\right]$ denotes the integral part of $x.$ Then range of $gof$ is

• A

  $[-1,1]$

• B

  $\left\{0\right\}$

• C

  $\{-1, 1\}$

• D

  $[0, 1]$