We have that $(X,\mathcal{A},\mu)$ is a measurable space and that $f\in L^{1}(\mu)$ .
and let $A\in\mathcal{A}$ and we want to make some estimations for the following intergral
$$\int_{A}\left | f \right |d\mu$$
Is it correct to assume that , because ($f\in L^{1}(\mu)$ $\Rightarrow$ $f$ is finite a.e and because $\left | f \right |\geq 0$) $\Rightarrow$ $\left | f \right |$ will have max , lets call it $M$.
Then $\int_{A}\left | f \right |d\mu\leq M\mu(A)$ ??