By the Lagrangian multiplier and constraint variational derivative, a
relationship between conserved quantities and multi-Hamiltonian
structures is built. Making using the relation a method is founded to
prove the infinite-dimensional Liouville integrability of evolution
equations with continuous variables. As the application, the
conservation laws of the Kundu equation are firstly obtained. Its
conserved quantities are deduced for comparing by Fokas' method
different from the method used in the existed literature. The
integrability of the equation is proved through taking the conservation
laws as a starting point.