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  "body": "\n## Statement\n\nLet $a \u003c b$ and let $f \\colon [a, b] \\to \\mathbb{R}$ be monotone.\nThen $f$ is Riemann integrable on $[a, b]$.\n\n## Remarks\n\nAssume $f$ increasing, and take the partition into $n$ equal pieces. Then $M_i = f(x_i)$ and $m_i = f(x_{i-1})$, so the sum telescopes:\n$$U(f, P) - L(f, P) = \\frac{b - a}{n} (f(b) - f(a)).$$\nThis tends to $0$, so [[Riemann's criterion|017DH8WXTE]] applies.\nA monotone function can have infinitely many discontinuities, and it is still integrable.\n\n## Explanations\n\n### L1 human\n\nFor an increasing function, the gaps between upper and lower rectangles stack up to one column of total height $f(b) - f(a)$.\nIts width shrinks to $0$ as the partition gets finer.\n",
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