This work is concerned about the privacy-preserving problem in reaching average consensus of continuous multi-agent systems. Given a network of integrators, some efficient protocols with integrable function based masking scheme are developed, where all agents communicate and then adjust their states by using the masked data so that their initial states are well protected from any external eavesdropper. Moreover, the study is also extended to cases with nonlinear couplings, which is further applied to the privacy-preserving phase synchronization of coupled Kuramoto oscillators. Our design is simple yet efficient for privacy-preservation, and brings more flexibility than some existing works. Numerical examples are presented for the purpose of demonstration and verification.