Answer
$\textbf{True}$
Work Step by Step
We are given that.
$$F'(x)= G'(x)$$
Integrating both sides from a to b gives,
$$\int^b_aF'(x)dx= \int^b_aG'(x)dx$$
Or
$$[F(x)+C]_a^b= [G(x)+C']_a^b$$
$$(F(b)+C)-(F(a)+C)= (G(b)+C')-(G(a)+C')$$
Therefore,
$$F(b)-F(a)=G(b)-G(a)$$
