In order to further improve the accuracy of the pseudospectral optimal control method, and weaken the amplification of approximation errors of state variables in the differential pseudospectral method, the integral pseudospectral optimal control method is studied. The integral pseudospectral discrete forms of three pseudospectral methods are presented, which are Legendre pseudospectral method, Gauss pseudospectral method and Radau pseudospectral method, respectively. When the approximation errors of Lagrange polynomials for state variables are equal to zero, it is proved that the differential and integral forms of Gauss pseudospectral method and Radau pseudospectral method are equivalent, but that of Legendre pseudospectral method is not equivalent, and the reason of nonequivalence is also analyzed.