On If $f(x)$ and $g(x)$ are Riemann integrable and $f(x)\leq h(x)\leq g(x)$, must $h(x)$ be Riemann integrable? it has been proven that the assumption given is false, but if $f$ and $g$ are both integrable on $[a,b]$ and $\int f(x)=\int g(x)$ , then is it now true that $h(x)$ is Riemann integrable? And if that happens to be the case, is $\int f(x)=\int h(x)$ on $[a,b]$?
2026-04-05 23:43:35.1775432615
As an addition to an aswered question.(Riemann integration)
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