For a real number y, let [y] denotes the greatest integer less than or equal to y. Then the function $f(x)=\large\frac{\tan(\pi[x-\pi])}{1+[x]^2}$ is

Question

$\begin{array}{1 1}(a)\;\text{discontinuous at some x}\\(b)\;\text{continuous at all x,but the derivative f'(x) does not exist for some x}\\(c)\;\text{f'(x) exists for all x,but the second derivative f'(x) does not exist for some x}\\(d)\;\text{f'(x) exists for all x}\end{array}$