Riemann Integral, Monontone

Question

Just a general question please, if a function is not monotone, can it still be Riemann Integrable?

Constant functions are also Riemann Integrable, right?

Thank you.

Continuous functions are Riemann integrable. – May 08 '17 at 10:31 — , May 08 '17 at 10:31
$\sin x$ is not monotone and it is Riemann integrable. – Crostul May 08 '17 at 10:37 — Crostul, May 08 '17 at 10:37

score 3 · Answer 1 · answered May 08 '17 at 10:34

All continuous functions (which includes all constant functions) are Riemann integrable on a closed interval, and there are many continuous functions that are not monotone, for example, $y=x^2$ on $[-1,1]$.

Riemann Integral, Monontone

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