How can Maxima integrate function with vector coefficient calculation in it?

Question

Say I have a function $f(t) = A t$ where $A \in \mathbb{R}^3$. I want to integrate it:

integrate(f(t), t, 0, 1);

it works and gives me 1 / 2 A, which is what I want.

However, if I type in:

integrate(f(t) . f(t), t, 0, 1);

it does not provide the result I want (actually it just output the integration mark). I was expecting something of 1 / 3 A . A.

How to guide Maxima to do this simplification? Or is it even possible?

I have pasted my code here:

(%i1) declare(A, nonscalar)
;
(%o1)                                done
(%i2) f(t) := A * t;
(%o2)                             f(t) := A t
(%i3) integrate(f(t), t, 0, 1);
                                       A
(%o3)                                  -
                                       2
(%i4) integrate(f(t) . f(t), t, 0, 1);
                                 1
                                /
                                [       <2>
(%o4)                           I  (A t)    dt
                                ]
                                /
                                 0