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  "body": "\n## Definition\n\nLet $I$ be an interval, let $f \\colon I \\to \\mathbb{R}$, and let $a, b \\in I$.\nAssume that $f$ is Riemann integrable on the closed interval between $a$ and $b$.\nThe definite integral of $f$ from $a$ to $b$ is the number $\\int_a^b f(x) \\, dx$ defined as follows.\nIf $a \u003c b$, it is the [[Riemann integral|0QM4TXT3DR]] of $f$ over $[a, b]$.\nIf $a = b$, it is $0$. If $a \u003e b$, it is $-\\int_b^a f(x) \\, dx$.\n\n## Remarks\n\nWith this sign convention, $\\int_a^b f + \\int_b^c f = \\int_a^c f$ holds for all $a, b, c$ in $I$.\nThe numbers $a$ and $b$ are the limits of integration, and $f$ is the integrand.\nMathlib writes the definite integral as `∫ x in a..b, f x`, through `intervalIntegral`.\n\n## Explanations\n\n### L1 human\n\nThe definite integral of $f$ from $a$ to $b$ is a number. It measures signed area under the graph between $a$ and $b$.\nThe order of the limits matters: swapping them changes the sign.\n",
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