The function $f(x)=[x]\cos\big[\large\frac{2x-1}{2}\big]$$\pi$ where [.] denotes the greatest integer function, is discontinuous at

Question

$\begin{array}{1 1}(a)\;\text{All x}&(b)\;\text{All integer points}\\(c)\;\text{No x}&(d)\;\text{x which is not an integer}\end{array}$