1.57 Comparison test for integrals

Let $f$ and $g$ be continuous real functions with $|f(x)|\leq g(x)\,$ for all $x\in(a,b)$, where $(a,b)$ may be finite or infinite. If the integral $\int_{a}^{b}g(x)dx$ converges, then the integral $\int_{a}^{b}f(x)dx$ also converges and satisfies