Is the integration on a compact Lie group invariant from left translation?

Question

Let G be a compact Lie group of dimension n and $ \Omega $ be a left-invariant n-form,$f:G \to \textbf{R}$ be a smooth map.

Is the equation below true? $$\int\limits_{\rm{G}} {f \circ \mu \left( {h, \cdot } \right)\Omega } = \int\limits_{\rm{G}} {f\Omega }$$ where $\mu(h,g)=hg$ is the multiplication in G.

If is,how to prove it?