Let $f:[0, \infty) \rightarrow[0, \infty)$ be defined as $f:(x)=\int_0^x[y] d y$ where $[x]$ is the greatest integer less than or equal to $x$. Which of the following is true?
Select the correct option:
A
$f$ is continuous at every point in $[0, \infty)$ and differentiable except at the integer points.
B
f is both continuous and differentiable except at the integer points in $[0, \infty)$.
C
$f$ is continuous everywhere except at the integer points in $[0, \infty)$.
D
f is differentiable at every point in $[0, \infty)$.
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