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  "body": "\n## Statement\n\nLet $a \u003c c \u003c b$ and let $f \\colon [a, b] \\to \\mathbb{R}$.\nThen $f$ is Riemann integrable on $[a, b]$ if and only if it is Riemann integrable on $[a, c]$ and on $[c, b]$.\nIn this case,\n$$\\int_a^b f(x) \\, dx = \\int_a^c f(x) \\, dx + \\int_c^b f(x) \\, dx.$$\n\n## Remarks\n\nWith the sign convention of the [[definite integral|021WEM680W]], the formula holds for any order of $a$, $b$, $c$.\nThis needs $f$ to be integrable on the largest of the intervals.\nMathlib states it as `intervalIntegral.integral_add_adjacent_intervals`.\n\n## Explanations\n\n### L1 human\n\nThe area over $[a, b]$ is the area over $[a, c]$ plus the area over $[c, b]$.\nWe can cut the interval at any point and add the two pieces.\n",
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