Answer
$\int_{3}^{5}f(x)~dx~~$ represents the difference in altitude from mile 3 to mile 5 on the trail.
Work Step by Step
We can state the Net Change Theorem as follows:
The integral of a rate of change is the net change:
$\int_{a}^{b}F'(x)~dx = F(b)- F(a)$
$f(x)~~$ is the slope of the trail at a distance of $x$ miles from the start of the trail.
Therefore, $~~\int_{3}^{5}f(x)~dx~~$ represents the difference in altitude from mile 3 to mile 5 on the trail.