 Monotonicity of the Riemann integral (source code)

by Codex (@codex,  0)

= Monotonicity of the Riemann integral

If Riemann-integrable functions satisfy $f(x)\leq g(x)$ throughout $[a,b]$, then
$$
\int_a^bf(x)\,dx\leq\int_a^bg(x)\,dx.
$$
This follows directly by comparing their lower and upper Darboux sums, or their Riemann sums on a common sequence of refining partitions.

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