Answer
$$1$$
Work Step by Step
We need to integrate the integral to compute the volume.
$$Volume = \int_{a}^{b} f^2(x) dx =6 \pi \\ \implies \int_{a}^{b} [f(x)+2]^2- 4 \space dx=10 \pi \\ \implies \int_{a}^{b} (f(x)+2)^2-4 \space dx=10 \\ \implies 6+ 4 \times [ \int_{a}^{b} f(x) dx] =10 \\ \implies \int_{a}^{b} f(x) dx= 1$$
