  By using some basic calculus of multiple integration, we provide an
alternative expression of the integral $$ \int_{]a,b[^n} f(\mathbf{x},\min
x_i,\max x_i) d\mathbf{x}, $$ in which the minimum and the maximum are replaced
with two single variables. We demonstrate the usefulness of that expression in
the computation of orness and andness average values of certain aggregation
functions. By generalizing our result to Riemann-Stieltjes integrals, we also
provide a method for the calculation of certain expected values and
distribution functions.
