Two techniques, based on the exchange of momentum and the integration of stress tensor, for the evaluation of the hydrodynamic forces in the lattice Boltzmann simulations are investigated on the curved and moving boundaries in two dimensions. The following results are obtained by numerical simulations: (i) the hydrodynamic forces on an inclined boundary and arc in liquid without flow computed by the stress-integration method agree with analytical predictions to a very high accuracy, while those by the momentum-exchange method have considerable errors for small segments; (ii) the simulation results of the sedimentation of a circular cylinder in a two-dimensional channel with the stress-integration method for hydrodynamic forces are in excellent agreement with those by a second-order moving finite-element method; (iii) the particle migrated from the centerline is found to occur in the simulations of a circular cylinder in a Poiseuille flow by the stress-integration method, consistent with the Segré-Silberberg effect. In conclusion, the stress-integration method can be a good candidate to evaluate the hydrodynamic forces on the elastic boundaries and moving particles in fluid.