If $f:R\to R$ is a function defined by $f\left(x\right)=\left[x\right]\mathrm{s}\mathrm{i}\mathrm{n}\left(\frac{2x-1}{2}\right)\pi ,$ where $\left[x\right]$ denotes the greatest integer function, then $f$ is

• A

  continuous for every real $x$
• B

  discontinuous only at $x=0$
• Correct answer
  C

  discontinuous only at integral values of $x$
• D

  continuous only at $x=0$

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