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  "body": "\n## Statement\n\nLet $I$ be an open interval, let $f \\colon I \\to \\mathbb{R}$ be continuous, and let $a \\in I$.\nThen $F(x) = \\int_a^x f(t) \\, dt$ is an [[antiderivative|0BW9N5CDSB]] of $f$ on $I$.\n\n## Remarks\n\nThe integral exists, since [[continuous functions are integrable|06SESV7GQY]]. The [[first fundamental theorem|063H5KJC69]] applies at each point of $I$.\nSo every continuous function on an open interval has an antiderivative.\nMathlib states the derivative as `Continuous.deriv_integral`.\n\n## Explanations\n\n### L1 human\n\nEvery continuous function has an antiderivative.\nThe area function from a fixed starting point is one.\n",
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