Generalizing the relation between H(x), F(x) and G(x)

If $H(x)= \int_c^x h(x)dx$ and $H(a) = F(a) - G(a) = \int_c^a h(x)dx$ and $H(b) = F(b) - G(b) = \int_c^b h(x)dx$, then does that mean $H(x) = F(x) - G(x)$? Is the information provided sufficient enough to come to that conclusion?

Simon Bridge