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  "body": "\n## Statement\n\nLet $a \u003c b$ and let $f \\colon [a, b] \\to \\mathbb{R}$ be continuous.\nThen $f$ is Riemann integrable on $[a, b]$.\n\n## Remarks\n\nBy the [[Heine–Cantor theorem|0W0TZDRF9C]], $f$ is uniformly continuous. Choose $\\delta$ for $\\varepsilon/(b - a)$. For a partition of mesh less than $\\delta$, $U(f, P) - L(f, P) \u003c \\varepsilon$. Then [[Riemann's criterion|017DH8WXTE]] applies.\nMore generally, a bounded function with finitely many discontinuities is Riemann integrable.\n\n## Explanations\n\n### L1 human\n\nOn short pieces of the interval, a continuous function changes very little.\nSo the upper and lower sums are close for fine partitions.\n",
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