JEE Math Practice Question

If $$f\left( {a + b - x} \right) = f\left( x \right)$$ then $$\int\limits_a^b {xf\left( x \right)dx} $$ is equal to

1. A.$${{a + b} \over 2}\int\limits_a^b {f\left( {a + b + x} \right)dx} $$
2. B.$${{a + b} \over 2}\int\limits_a^b {f\left( {b - x} \right)dx} $$
3. C.$${{a + b} \over 2}\int\limits_a^b {f\left( x \right)dx} $$
4. D.$$\,{{b - a} \over 2}\int\limits_a^b {f\left( x \right)dx} $$