The integral expression is .

Consider .

Assume .

Apply derivative on each side.

.

Change of integral limits :

Lower limit: If  then .

Upper limit: If  then .

Substitute ,  and change of limits in .

.

Replace the variable  with .

.

Hence it is verified.

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Prove the above expression, graphically by considering the example function .

Consider the lower and upper limits as  and .

Consider the constant  as .

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Here we need to prove,.

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

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