Question 7
Let $a \lt c \lt b$ be real numbers and let $f : [a, b] \to \mathbb{R}$ be a function continuous at $c$. Show that if $f$ is the derivative of a function $F_a$ on $[a, c)$, and also the derivative of a function $F_b$ on $(c, b]$, then $f$ is the derivative of some function $F$ on the entire interval $[a, b]$.