Difference quotient integration property

Question

Let us define: $$D^{h}_{k}u(x) = \frac{u(x+he_{k})-u(x)}{h} \quad (h\in \mathbb{R}, h\neq 0)$$ for $u : \mathbb{R}^{n} \to \mathbb{R}$ and $e_{k} = (0,0,...1,...0)$ is a vector in $\mathbb{R}^{n}$ with zero as the value of all components except for the k-th component which is 1.

The problem with this is I can't get a proper definition when $h<0$. Is this true that given $h>0$ then $$D^{-h}_{k}u(x) = \frac{u(x-he_{k})-u(x)}{-h} \quad (h\in \mathbb{R}, h\neq 0)$$like that?
I want to prove $\int_{U}D^{h}_{k}u(x)v(x)dx = -\int_{U}u(x)D^{-h}_{k}v(x)dx$ but I don't know where to start.
Any help is much appreciated!