Integration for $\int_a^b f(k-x)dx$ Knowing that $\int_a^b f(x) dx=F(b)-F(a)$. What if $\int_a^b f(k-x)dx$ assuming k is a constant which is always greater than x, a, and b? 

Observe that
$$\frac{\mathrm d}{\mathrm dx}k - x = -1$$
Therefore
$$\int_a^bf(k - x)\mathrm dx = -\int_a^b-f(k - x)\mathrm dx = -\left[F(k - x)\right]_a^b = F(k - a) - F(k - b)$$
