The problem is that if you use symbolic "y" and "h" in your way, it will not give you the result.
But if you put "h" equal to specific number and then you can find the integral of this function without boundaray "-y" and "y". Then, you can substitute value of "x = -y" and "x = y" into the obtained integral.
syms b x
h = 2;
f = int(G,x)
It will give
Then, we can find the integral from -y to y by substitute them into the above function
fy = subs(f,y) - subs(f,-y)
and we obtain
By that way, you can change the value of "h = 3, 4, ....".