Suppose $\displaystyle f$ is a riemann integrable function on $\displaystyle [a,b].$ If $\displaystyle g$ is a bounded real valued function defined on $\displaystyle [a,b]$ and $\displaystyle g$ differs from $\displaystyle f$ at infinitely many points in $\displaystyle [a,b]$, should $\displaystyle g$ be riemann integrable on $\displaystyle [a,b]$. Prove or disprove?