$f\left(x\right)=\left[x^2\right]-{\left[x\right]}^2$ , then (where [.] denotes greatest integer function)

f is not continuous $x=0andx=1$

f is continuous at   $x=0$ but not at  $x=1$

f is not continuous at  $x=0$ but continuous at  $x=1$

f is continuous at $x=0$ and  $x=1$