Suppose $M$ is an $m-$dimensional oriented smooth manifold and that $\omega \in \Omega_c^m(M)$ be a smooth $m-$form with compact support. I want to understand the definition of integral of $\omega$ at the chart $(U,\varphi)$. The definition that is given is $$ \int_U \omega := \int_{\mathbb{R}^m} a(x_1,\cdots,x_m)\ d\mu(x_1)\cdots d\mu(x_m) $$ where $a \ dx_1\wedge \cdots \wedge dx_m = (\varphi^{-1})^*(\omega)\in\Omega_c^m(\varphi(U))$ and $a\in C^\infty(\varphi(U))$ is smooth with compact support.
My question is: I don't understand $d\mu(x_i)$ in the expression in the RHS of above definition. What are $d\mu(x_i)$? Can someone help me by explaining the definition in simpler terms?