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