The integral expression is .

Consider .

Assume .

Apply derivative on each side.

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Change of integral limits:

Lower limit: If then .

Upper limit: If then .

Substitute , and change of limits in .

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Property of definite integral: .

Replace the variable with .

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Hence it is verified.

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Graphically verify the above expression.

Consider an example function .

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Consider the lower and upper limits as and .

Here we need to prove,.

Graphically the areas of the regions under the curve are same and the value is  .

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