with(linalg):
f:=[y,-x^3+x+(3/2)*x^2+y-x^2*y];
G:=subs(x=x(t),y=y(t),f);
(Note: substitute your parametrization of the circle for x(t) and y(t) in the above.)
Q:= innerprod(G,n);
int( stuff_to_integrate, t=0..2*Pi);