At how many points in the open interval $(-3, 3)$ is $f(x) = \sin(\pi[x])$ not continuous?

Explanation

1. 01

   $[x]$ is always an integer $n$, and $\sin(n\pi) = 0$ for every integer $n$.

2. 02

   So $f(x) = 0$ for every $x$, a constant function, continuous everywhere: 0 points.