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Prove that int(a)^(b)f(x)dx=(b-a)int(0)^...

Prove that `int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx`

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`I=(b-a)int_(0)^(1)f((b-a)x+a)dx`
Let `(b-a)x+a=t`
`impliesdx=(dt)/((b-a))`
`impliesdx=(dt)/((b-a))`
Also when `x=0` then `t=a` an `x=1` then `t=b`
`:.I=(b-a)int_(a)^(b)f(t)(dt)/((b-a))`
`=int_(a)^(b)f(t)dt`
`=int_(a)^(b)f(x)dx` (Change of dummy variable)
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