7.1. Riemann Integral

Examples 7.1.18(a):

Show that every monotone function defined on [a, b] is Riemann integrable.
We have shown before that a monotone function f defined on a closed interval [a, b] has at most countably many discontinuities.

Therefore such a function f is continuous except at countably many points, so that by our previous theorem the function must be Riemann integrable.

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