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int (a) ^(b) f (x) dx = int (a) ^(b) f (...

`int _(a) ^(b) f (x) dx = int _(a) ^(b) f (a + b - x) dx `

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Let f(x) and g(x) be any two continuous function in the interval [0, b] and 'a' be any point between 0 and b. Which satisfy the following conditions : f(x)=f(a-x), g(x)+g(a-x)=3, f(a+b-x)=f(x) . Also int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx, int_(a)^(b)f(x)dx=int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx If f(a+b-x)=f(x) , then int_(a)^(b)xf(x)dx is