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  "body": "\n## Summary\n\nFor a nonnegative continuous function $f$ on $[a, b]$, the area under its graph is the [[integral|0QM4TXT3DR]] $\\int_a^b f(x) \\, dx$. The integral approximates the region by thin rectangles, through [[Riemann sums|0HBY48G8G1]]. For a function of any sign, the integral counts area below the $x$-axis as negative.\n\n## Remarks\n\nThe area between the graphs of $f \\le g$ over $[a, b]$ is $\\int_a^b (g(x) - f(x)) \\, dx$.\nFor example, the area under $x^2$ over $[0, 1]$ is $1/3$. In the 3rd century BC, Archimedes found the area under a parabola by the method of exhaustion.\nThe [[fundamental theorem of calculus|0NHGY0N0JB]] computes areas from antiderivatives.\n\n## Explanations\n\n### L1 human\n\nThe integral measures the area of the region under a graph.\nWe fill the region with thin rectangles and add up their areas.\n",
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