Question

Why is the answer true?

Answer 1

Hello, one way to see it is as below

$\displaystyle F(2)-F(1)=\int_1^2 F'(t) dt=\int_1^2 G'(t) dt=G(2)-G(1)$

Another way is to notice that F'(x)=G'(x) means that F(x) and G(x) are only different from a real constant that we can note a, it means that

$(\forall x \in \mathbb{R}) \ (F'(x)=G'(x)) => (\exists a \in \mathbb{R});(F(x)=G(x)+a)$

and then F(2)-F(1)=G(2)-G(1)

thanks