How can I do this 'Double integral having only one variable' fast?

Dear all, I have a function as follows: f(x) = integral(integral(g(x),0,x)*integral(h(x),0,x),a,b). Here, g(x) and h(x) are arbitrary functions of x. a and b are arbitrary integral range. I've tried to do it using Gaussian quadrature twice. But it is kind of complicated and I thought there would be some more clever ways to do it. I need to calculate it as fast as possible. Could you please help me?