Answer
The change in the child’s weight (in pounds) between the ages of 5 and 10
Work Step by Step
The problem states that $w'(t)$ is the rate of growth of a child in pounds every year. This makes $w(t)$ the amount of pounds that the child grew by. In this case, the integral $\int_5^{10} w'(t) dw$ looks at the years $5$ and $10$ of the child's growth. Since $\int w'(t) dw = w(t)$, $\int_5^{10} w'(t) = w(10) - w(5)$ by the formula $$\int_a^b w'(t) = w(b) - w(a)$$
Therefore, we get the change in the child’s weight (in pounds) between the ages of 5 and 10