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  "body": "\n## Definition\n\nLet $P$ and $Q$ be [[partitions|069P20KYQT]] of $[a, b]$.\nThe partition $Q$ is a refinement of $P$ if each point of $P$ is also a point of $Q$.\n\n## Remarks\n\nAny two partitions $P$ and $Q$ have a common refinement, made of the points of both.\nRefining a partition lowers the upper [[Darboux sum|0QRQVH0CRW]] and raises the lower Darboux sum, or leaves them unchanged.\n\n## Explanations\n\n### L1 human\n\nA refinement cuts the interval at more points.\nEach old subinterval is cut into one or more new subintervals.\n",
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