Answer
True, see explanations.
Work Step by Step
Based on the Fundamental Theorem of Calculus, given a function $y=f(x)$ that is differentiable on $[a,b]$, we know it is continuous on $[a,b]$, and we can define $F(x)=\int_a^x f(t)dt$ which gives $F'(x)=f(x)$. This shows that $f(x)$ is a derivative of $F(x)$, so the statement is true.
