Answer
$2$
Work Step by Step
Integrate the integral to calculate the volume as follows:
we have: $V= \pi \times \int_{a}^{b} f^2(x) dx =4 \pi$
or, $ \int_{a}^{b} (f(x)+1)^2-1 dx=8$
or, $ 4+(2) \int_{a}^{b} f(x) dx=8$
Thus, our answer is: $\int_{a}^{b} f(x) dx= 2$
