About Law of Large Numbers

Question

I would like to understand why $$ \frac{1}{M}\sum_{k=1}^M \mu (X_t^k, U_t^k) \cdot h \to \mathbb{E}\left[\int_\mathcal{U} \mu(X_t^\pi, u)\pi_t(u) \ \text{d} u \cdot h\right], $$ by the Large of Large Numbers as $M\to\infty$. Here $X^1,\ldots, X^M$ is a sample which has been obtained by $X^\pi$, where $\pi$ indicates that each $X^k$ is generate according to $$ \text{d} X_t^U = \mu(X_t^U, U_t) \text{d} t + \sigma(X_t^U, U_t)\text{d}W_t $$ with the corresponding $U^k$ sampled directly under the distribution induced by $\pi$. Particulary, I don't understand why the integral appears. Any hint, please?