How to integrate this double integral?

Hi, i try to integrate: Int( dy Int(dx G(x), t0, y), t0, t). Where G(x) is a function which accepts a vector, also t is a vector. y is depending on the outer integral. I tried it with trapez ( the integral value have not 100% exact) but it is too slow :(. Any suggestions how this integral can be implemented efficiently.

Here my slow code:

for j = 2:length(t)
    Xj = t(1:j);

      Yj = zeros(size(Xj));
      for j = 1:length(Yj)
          Yj(j) = trapz(1:Xj(j),G(1:Xj(j)));
      end  

      y(j) = trapz(Xj,Yj);

end

Thank you!