At how many points in the open interval $(-2, 3)$ is the greatest integer function $f(x) = [x]$ not continuous?

Explanation

1. 01

   $[x]$ jumps by 1 at every integer and is continuous elsewhere.

2. 02

   The integers strictly between $-2$ and 3 are $-1, 0, 1, 2$: 4 points.