Is every function that can be integrated using Riemann integral must be monotonic function?
If false then is there an example.
2026-04-03 04:01:57.1775188917
Is every function that can be integrated using Riemann integral must be monotonic function?
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No. $\sin(x)$ is Riemann integrable between $0$ and $\pi$. In fact, any non-monotone continuous function on a compact set.
An example of a nowhere monotone continuous function is given in this answer. (A function is nowhere monotone if there is no nonempty open set on which it is monotone.)