JEE Math Practice Question

If ƒ(a + b + 1 - x) = ƒ(x), for all x, where a and b are fixed positive real numbers, then $${1 \over {a + b}}\int_a^b {x\left( {f(x) + f(x + 1)} \right)} dx$$ is equal to:

1. A.$$\int_{a - 1}^{b - 1} {f(x+1)dx} $$
2. B.$$\int_{a + 1}^{b + 1} {f(x + 1)dx} $$
3. C.$$\int_{a - 1}^{b - 1} {f(x)dx} $$
4. D.$$\int_{a + 1}^{b + 1} {f(x)dx} $$