The generating function of the Segre integrals on Hilbert schemes of points on a surface X can be determined by five universal series A_0, A_1, A_2, A_3, A_4, due to the result of Ellingsrud-Göttsche-Lehn. These five series do not depend on the surface X, and depend on the element of K(X) to which the Segre integrals are associated, only through the rank. Marian-Oprea-Pandharipande have determined A_0, A_1, A_2 for all ranks. For rank 0, it is easy to see A_4=1. They also conjectured that A_3 = A_0A_1 for rank 0. We prove this conjecture by showing that when X is the projective plan, the Segre integrals associated to the structure sheaf of a curve in the anti-canoncial class are all zero. Very recently Göttsche-Mellit have obtained the explicit expression for A_3 for all rank r >2 using localization, and hence by polynomiality their result also gives the expression for A_3 for all ranks. But our method is totally different from theirs and contains more geometric concept.