If \( f(a+b+1-x)=f(x) \), for all \( x \), where \( a \) and \( b \) are fixed positive real numbers, then \( \frac{1}{a…

If \( f(a+b+1-x)=f(x) \), for all \( x \), where \( a \) and \( b \) are fixed positive real numbers, then \( \frac{1}{a+b} \int_{a}^{b} x(f(x)+f(x+1)) d x \) is equal to

[JEE Main 2020, 7 Jan (Shift 1)]