Poincaré-Cartan Integral Invariant for Singular Nth-order Lagrangian

A generalization of Poincaré-Cartan integral invariant for singular Nth-order Lagrangian whose constraints are dependent on time explicitly was given. The connection between this invariant and canonical equations were discussed. Some confusions in the literature were corrected. The Poincaré-Cartan integral invariant provide a useful tool to research the Dirac's conjecture for the system with singualr Nth-order Lagrangian.