# splitting integral over a product space

Let $M=[0,a]\times\mathbb{R}$ with the Lebesgue measure and let $f:M\rightarrow \mathbb{R}$ be a positive function.

Is it true that $$\int_M f(x,y)\; dx\; dy = \int_{[0,a]}\Big(\int_{\mathbb{R}} f(x,y)\; dy\Big) \; dx= \int_\mathbb{R}\Big(\int_{[0,a]} f(x,y)\; dx\Big)\; dy\quad ?$$