Sum of functions is Riemann integrable implies that the functions are Riemann integrable?

Question

If $f,g: [a,b] \to \mathbb{R}$ are bounded, if $f+g$ is Riemann integrable does this imply that $f$ and $g$ are Riemann integrable?

Answer 1

If $f$ is not Riemann integrable and you let $g=-f$, what happens?