The function $f(x)=[x]^2-[x^2]$ where $[x]$ is the greatest integer less than or equal to x, is discontinuous at

Question

$\begin{array}{1 1}(a)\;\text{all integers}\\(b)\;\text{all integers except 0 and 1}\\(c)\;\text{all integers except 0}\\(d)\;\text{all integers except 1}\end{array}$