If $f:R\to R$ is a function defined by $f(x)=[x]\cos\big(\large\frac{2x-1}{2}\big)$$\pi$ where [x] denotes the greatest integer function then f is

Question

$\begin{array}{1 1}(a)\;\text{continuous for every real x}\\(b)\;\text{discontinuous only at x=0}\\(c)\;\text{discontinuous only at non-zero integral values of x}\\(d)\;\text{Continuous only at x=0}\end{array}$