I am solving $I = \int_{0}^{1}f(x)dx$ by Monte Carlo, e.g $I = E[f(U)]$ where $U\sim unif([0,1])$ so have
$I = E[f(U)]\approx \hat I_M\colon= \frac{1}{M}\sum_{m=1}^Mf(u_m)$
I am interested in how quickly $\hat I_M$ converges to $I$, i.e. how quickly $|\hat I_M - I|\rightarrow 0$ as $M\rightarrow \infty$. I do not understand in which convergence sense I am looking at? Is it in simply in 'absolute convergence sense'?
Thanks in advance for any help!