In experimental aerodynamics (and hydrodynamics) it is well known that, if the flow past a solid body is steady, then the total force on the body can be conveniently estimated by the measured flow data on an appropriate control surface alone. We now show that, for the first time, the steady-flow condition can be removed provided that the flow is incompressible: two innovative formulas for the total force acting on any solid body that moves and deforms arbitrarily in a viscous incompressible fluid, solely in terms of control-surface integrals, are derived based on derivative-moment transformations. The formulas are verified by a numerical test for flow over a two-dimensional fishlike swimming body.