If f(a+b+1-x)=f(x), for all x where a an...

If `f(a+b+1-x)=f(x)`, for all x where a and b are fixed positive real numbers, the `(1)/(a+b) int_(a)^(b) x(f(x)+f(x+1))` dx is equal to :

A

`int_(a+1)^(b + 1) f(x + 1) dx`

B

`int_(a-1)^(b-1) f(x + 1) dx`

C

`int_(a+1)^(b+1) f(x) dx`

D

`int_(b-1)^(a-1) f(x) dx`

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The correct Answer is:

C

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