Plotting a function with a variable distributed uniformly

I am trying to plot the following as a function of $s$:
$$ u_f= frac{P(S-s)sigma_i}{n_f(s)}+H(s) $$
where $sigma_i$ is distributed uniform on the interval $[sigma_l,sigma_h]$, and $s in [0,S]$. Can someone help me with how to define the $sigma_i$ term with this distribution (plotting with any arbitrary numbers for $sigma_l$ and $sigma_h$.