You can call intergal2() twice like shown in this example
f = @(x,y,z,w) x.^2+(y.*z)+w;
% limits:
% x: [0 2]
% y: [0 3]
% z: [5 9]
% w: [1 3]
I1 = @(Z, W) arrayfun(@(z,w) integral2(@(x,y) f(x,y,z,w), 0, 2, 0, 3), Z, W);
integral2(@(z,w) I1(z,w), 5, 9, 1, 3)