Can Maxima solve this optimization problem?

Dear All,

I am trying to solve the following maximization problem with Maxima:

find x(t) (continuous) that maximizes the

integral of x(t) with t from 0 to 1,

subject to the constraints

dx/dt = u,

|u| <= 1,

x(0) = x(1) = 0.

The analytical solution can be obtained easily, but I am trying to
understand whether Maxima is able to solve numerically problems like
this one. I have tried to find an approximate solution through
discretization of the objective function but with no success so far.

Thanks in advance,

Paul