Calculate the integral without knowing the integrand How can I calculate this integral?

$$\int_0^{2014} \frac{f(x)}{f(x) + f(2014 - x)}dx$$


Note that for $b=2014$, the object you want is
$$W:=\int_0^b \frac{f(x)}{f(x)+f(b-x)} dx = 
\int_0^b \frac{f(x)+f(b-x)}{f(x)+f(b-x)} dx - \int_0^b \frac{f(b-x)}{f(x)+f(b-x)} dx\\
= b - \int_0^b \frac{f(b-x)}{f(x)+f(b-x)} dx.$$
Now, by substitution of $t=b-x$,
$$
\int_0^b \frac{f(b-x)}{f(x)+f(b-x)} dx =
-\int_b^0 \frac{f(t)}{f(b-t)+f(t)} dt=\int_0^b \frac{f(t)}{f(t)+f(b-t)}dt.
$$
So plugging that back into the first equation we get $W=b-W$, such that $W=b/2$.
