for A being non empty closed_interval Subset of REAL
for rho, rho1, rho2 being Function of A,REAL
for u being PartFunc of REAL,REAL st rho is bounded_variation & rho1 is bounded_variation & rho2 is bounded_variation & dom u = A & rho = rho1 - rho2 & u is_RiemannStieltjes_integrable_with rho1 & u is_RiemannStieltjes_integrable_with rho2 holds
( u is_RiemannStieltjes_integrable_with rho & integral (u,rho) = (integral (u,rho1)) - (integral (u,rho2)) )