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  "body": "\n## Definition\n\nLet $a \u003c b$ and let $f \\colon [a, b] \\to \\mathbb{R}$ be a function.\nThe function $f$ is a step function if it is constant on each open subinterval of some [[partition|069P20KYQT]] $(x_0, \\dots, x_n)$ of $[a, b]$.\nThat is, there are real numbers $c_1, \\dots, c_n$ with $f(x) = c_i$ for all $x \\in (x_{i-1}, x_i)$.\n\n## Remarks\n\nThe values of $f$ at the points $x_i$ are arbitrary.\nA step function is Riemann integrable, and $\\int_a^b f = \\sum_{i=1}^{n} c_i (x_i - x_{i-1})$.\nThe floor function $\\lfloor x \\rfloor$ restricted to $[a, b]$ is a step function.\n\n## Explanations\n\n### L1 human\n\nThe graph of a step function looks like a staircase.\nIt is flat on each piece of a partition, and it can jump at the cut points.\n",
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