Part b
Given the derivative function \(f'(x) = 2x\) over the interval [1, 3], use integration to calculate the net change in \(f(x)\) between \(x = 1\) and \(x = 3\).
Part c
Discuss how the area under the graph of the derivative \(f'(x)\) corresponds to the net change in \(f(x)\) and provide a real-world example where this relationship is useful.