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  "body": "\n## Definition\n\nLet $a \u003c b$ and let $f \\colon [a, b] \\to \\mathbb{R}$ be [[Riemann integrable|0N1JQXZXHC]].\nThe Riemann integral of $f$ over $[a, b]$ is the unique number $I$ in the definition of Riemann integrability.\nIt is written\n$$\\int_a^b f(x) \\, dx.$$\n\n## Remarks\n\nFor $f \\ge 0$, the integral equals the area under the graph of $f$ and above the $x$-axis.\nBy convention, $\\int_a^a f = 0$ and $\\int_b^a f = -\\int_a^b f$.\nThe [[fundamental theorem of calculus|0NHGY0N0JB]] computes the integral from an antiderivative.\nThe integral is named after Bernhard Riemann.\n\n## Explanations\n\n### L1 human\n\nThe Riemann integral is the limit of sums of areas of thin rectangles under the graph.\nIt gives the signed area between the graph and the $x$-axis.\n",
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