Suppose we have a random variable $Y$ distributed uniformly over the interval $[-1,1]$ with pdf $p(y) \equiv 1/2.$ Furthermore, we have another function $G(2y-k)$ for some constant $k.$ Can you then simplify the following expression any further?
$$\int_k^1 G(2y-k) p(y) \, dy + \int_{-1}^k G(2y-k) \, dy$$
By 'simplify' I mean sth like 'using the integral sign just once'. The idea is that $G(2y-k) p(y)$ is just a linearly scaled version of $G(2y-k)$ and therefore I thought there could be a way of redefining the equation?