# Relation between two functions defined by and integral

Let us consider the two functions $$F(x) = \int\limits_x^1 {h(s - x,s)ds - } \int\limits_{1 - x}^1 {h(2 - s - x,s)ds}$$$$G(x) = \int\limits_0^x {h(x - s,s)ds - } \int\limits_0^{1 - x} {h(x + s,s)ds}$$ Where $$h$$ is some regular function. Note that $$F(0)=-G(0)$$, and $$F(1)=-G(1)$$. But I can not find a general relation between these two functions. I will be grateful to yiur helps. Thank you.

• Could you share your thoughts, why you think there should be a general relation linking the two functions directly? – maxmilgram Jan 11 at 12:03
• I have some intuition about that by I'm not sure. I've made many of variable substation but I didn't succeed. – Gustave Jan 11 at 12:05