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.

Answer 1

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 $[-1,1]$.