$\"\"$

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The function is $\"\"$ on interval is $\"\"$ .

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Number of rectangles are $\"\"$ .

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The sum of all inscribed rectangle is lower sum.

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$\"\"$ , where $\"\"$

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The sum of all circumscribed rectangle is upper sum.

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$\"\"$ , where $\"\"$

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Where $\"\"$ .

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$\"\"$

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Find lower sum.

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$\"\"$ .

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Area of lower sum is $\"\"$ .

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$\"\"$

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Sum of natural numbers is $\"\"$ .

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$\"\"$

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$\"\"$

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Find upper sum.

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$\"\"$ .

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Area of higher sum is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Verification:

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$\"\"$

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$\"\"$

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$\"\"$