Adding increasing function to an integral

Suppose the following holds for a continuous f(x) defined on the real line: $$\int_{-\infty}^{+\infty}f(x)dx\geq 0$$

where $f(x)$ can take both positive or negative values.

Suppose there is a function $g(x)$ defined on the entire real line where $g(x)$ is strictly increasing and $g(x)>0$ for all $x$. Does it follow that $\int_{-\infty}^{+\infty}f(x)g(x)dx\geq 0$? Thank you!