Answer
TRUE
Work Step by Step
Given: $f(x)\geq g(x)$
This implies
$f(x)-g(x)\geq 0$
$\int _{a}^{b}[f(x)-g(x)] dx\geq 0$
$\int _{a}^{b}f(x) dx-\int _{a}^{b}g(x) dx\geq 0$
$\int _{a}^{b}f(x) dx\geq \int _{a}^{b}g(x) dx$
Hence, the statement is true.