Answer
$f(x)$ is continuous over an infinite number of intervals of the form:
$(n, n+1)$ where $n$ is an integer.
Work Step by Step
$f(x)=[[x+3]].$
$f(x)$ has a nonremovable discontinuity at every integer value of $x$ but is continuous in between consecutive integer values.
This shows that $f(x)$ is continuous over $(n, n+1)$ where $n$ is any integer.
