Show that the histogram estimator is an unbiased estimator

Question

So the question is asking to show that the histogram estimator $\mathbb{E}_p[\hat{p}_n(x)]$ is unbiased. So I worked and found that the histogram estimator is $$\hat{p}_n(x)=\sum_{j=1}^{m}(\frac{\hat{p}_j}{h}indicator(x\in B_j))$$ Where m is the number of chosen bins for the histogram and $B_j$ is like this: $$mbins: B_1 = [0,\frac{1}{m}), B_2 = [\frac{1}{m},\frac{2}{m}),.....B_m=[\frac{m-1}{m},1]$$ Furthermore, the bandwidth $h = \frac{1}{m}$, $\hat{p}_j=\frac{Y}{n}$ with $Y_j=$ the number of observations in $B_j$....... Now I understand that I am supposed to integrate the histogram estimator that I obtained since it is a continuous random variable. But I do not understand where to begin or even what the bounds are. Any help would be appreciated. Thank you.