Answer
$[0,1)\cup(1,2)\cup(2,3)\cup(3,4]$
Work Step by Step
In the point $x=1$ the function is undefined, therefore $f$ is not continuous in $x=1$.
In the point $x=2$, $\lim\limits_{x \to 2} f(x)=3$, $f(2)=2$, therefore $f$ is not continuous in $x=2$.
In the point $x=3$, $\lim\limits_{x \to 3^-} f(x)=0$, $\lim\limits_{x \to 3^+} f(x)=1$, so $\lim\limits_{x \to 3} f(x)$ doesn't exist, therefore $f$ is not continuous in $x=3$.
The intervals of continuity are:
$[0,1)\cup(1,2)\cup(2,3)\cup(3,4]$
