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  "body": "\n## Statement\n\nLet $f, g \\colon [a, b] \\to \\mathbb{R}$ be Riemann integrable, and let $\\alpha, \\beta \\in \\mathbb{R}$.\nThen $\\alpha f + \\beta g$ is Riemann integrable on $[a, b]$, and\n$$\\int_a^b (\\alpha f(x) + \\beta g(x)) \\, dx = \\alpha \\int_a^b f(x) \\, dx + \\beta \\int_a^b g(x) \\, dx.$$\n\n## Remarks\n\nThe [[Riemann sums|0HBY48G8G1]] satisfy $S(\\alpha f + \\beta g, P, t) = \\alpha S(f, P, t) + \\beta S(g, P, t)$. Pass to the limit.\nSo the Riemann integrable functions on $[a, b]$ form a vector space, and the integral is a linear map on it.\nMathlib states additivity as `intervalIntegral.integral_add`.\n\n## Explanations\n\n### L1 human\n\nThe integral of a sum is the sum of the integrals.\nConstant factors can move out of the integral.\n",
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