Question: Let $f(x) = 0$ if $x \neq 1$, and $f(x) = 1$ if $x=1$ Let $F(x) = \int_0^xf $. At which points is $F'(x) =f(x)$?
Answer Can I get a check to see if my answer is correct?
I understand that if a function $g$ is integrable on $[a,b]$, and we let $h = g$ except at finitely many $x_i \in [a,b]$, then $h$ is still integrable, and $\int_a^b g = \int_a^b h$.
Thus in the above question $F'(x)=0$ for all $x$, so $F'(x)=f(x)$ for all points except $x=1$.