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If $f(a + b + 1 - x) = f(x)$, for all $x$, where $a$ and $b$ are fixed positive real numbers, then $\dfrac{1}{a + b}\int_a^b x(f(x) + f(x + 1)),dx$ is equal to:
(1) $\int_{a+1}^{b+1} f(x),dx$
(2) $\int_{a-1}^{b-1} f(x),dx$
(3) $\int_{a-1}^{b-1} f(x + 1),dx$
(4) $\int_{a+1}^{b+1} f(x + 1),dx$
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