  Applying the Picard-Fuchs equation to the discontinuous differential system,
we obtain the upper bounds of the number of zeros for Abelian integrals of four
kinds of quadratic differential systems when it is perturbed inside all
discontinuous polynomials with degree $n$. Furthermore, by using the {\it
Chebyshev criterion}, we obtain the sharp upper bounds on each period annulus
for $n=2$.
