There is currently no built-in functionality to integrate over time. You would have use the toolbox with Matlab, export your data (
https://www.featool.com/doc/post#postex), and perform the integration there (
https://www.featool.com/doc/intbdr_8m), for example something like:
val = 0;
ind_b = array_of_boundary_numbers_to_integrate
for i_sol=1:length(fea.sol.t)
val = val + intbdr( 'rho_ns*(nx*u+ny*v)', fea, ind_b, 2, i_sol );
end
dt = fea.sol.t(end) - fea.sol.t(1);
result = val / dt