Let $U \subseteq \mathbb{R}^n$ be a bounded open set with $C^1$ boundary $\partial U$, and let $u \in C^1(\overline{U})$. Then for each $i = 1, \dots, n$, \begin{align*} \int_U \frac{\partial u}{\partial x_i}(x) \, d\mathcal{L}^n(x) = \int_{\partial U} u(x) \, \nu^i(x) \, d\mathcal{H}^{n-1}(x), \end{align*} where: - $\mathcal{L}^n$ denotes $n$-dimensional Lebesgue measure on $\mathbb{R}^n$, - $\mathcal{H}^{n-1}$ denotes $(n-1)$-dimensional Hausdorff measure on $\mathbb{R}^n$, restricted to $\partial U$, - and $\nu(x) = (\nu^1(x), \dots, \nu^n(x))$ is the outward unit normal to $\partial U$ at $x$.