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

Question

${{a + b} \over 2}\int\limits_a^b {f\left( {a + b + x} \right)dx} $

${{a + b} \over 2}\int\limits_a^b {f\left( {b - x} \right)dx} $

${{a + b} \over 2}\int\limits_a^b {f\left( x \right)dx} $

$\,{{b - a} \over 2}\int\limits_a^b {f\left( x \right)dx} $

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