What does evaluating a definite integral where the limits are functions represent?

Question

I understand that FTC claims:

$$ \int_a^bf(t)dt = F(b) - F(a) \text{ ,where a and b are functions}$$

What does $F(b) - F(a)$ mean/represent?

Answer 1

If $F(x)$ is primitive function of $f(x)$ then $F'(x)= f(x)$ and $$\int_a^bf(t)dt= F(x)\Big|^b_a = F(b)-F(a)$$

Answer 2

These stand for antiderivatives, that is $F' = f$. We can pick an arbitrary such antiderivative (why?).