Riemann Integrability of Composite functions.

Function $f$ is continuous and strictly increasing on $[a,b]$ and $g$ is Riemann integrable such that $g \circ f$ is defined. Is $g \circ f$ Riemann integrable?

I was able to show that if $f$ additionally satisfies:
$x_{1},x_{2} \in [a,b] \Rightarrow f(x_2)-f(x_1) \geq x_{2}-x_{1}$, then $g \circ f$ is Riemann integrable.

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