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If int(0)^(100) f(x)dx=7, then sum(r=1)^...

If `int_(0)^(100) f(x)dx=7,` then `sum_(r=1)^(100)int_(0)^(1)(r-1+x)dx=`_________.

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The correct Answer is:
7
`sum_(r=1)^(100)(int_(0)^(1)f(r-1+x)dx)`
`=int_(0)^(1)f(x)dx+int_(0)^(1)f(1+x)dx+int_(0)^(1)f(2+x)dx+………….+int_(0)^(1)f(99+x)dx`
`=int_(0)^(1)f(x)dx+int_(1)^(2)f(x)dx+int_(2)^(3)f(x)dx+……….+int_(99)^(100)f(x)dx`
`=int_(0)^(100)f(x)dx=7`
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