Answer
$$2$$
Work Step by Step
We need to integrate the integral to compute the volume.
We have:
$$Volume = \int_{a}^{b} f^2(x) dx \times \pi =4 \pi \\ \implies \int_{a}^{b} (f(x)+1)^2-1 dx=8 \\ \implies 4+(2) \int_{a}^{b} f(x) dx=8 \\ \implies \int_{a}^{b} f(x) dx= 2$$
