If $f'$ is piecewise smooth on $[a,b]$, then $f$ is piecewise smooth on $[a,b]$.
Is this statement true?
I know that if we let $f'$ be piecewise smooth on $[a,b]$. Then, by definition, both $f'$ and $f''$ are piecewise continuous on $[a,b]$. Now, what I am left to show is that $\int f'$ is piecewise continuous on $[a,b]$.
In other words, is the anti-derivative of a piecewise continuous function also piecewise continuous?
Thanks in advance!