integrate(sin(x)*cos(x),x) I got a solution

assume  (t>0);
integrate(cos(x)*sin(x),x,0, t);
trigsimp(%);
    

Calculated in 0.09171 seconds.
(%i1)                  assume(t > 0)
(%o1)                     [t > 0]
(%i2)                integrate(cos(x) sin(x), x, 0, t)
                     2
                  1   cos (t)
(%o2)                   - - -------
                  2     2
(%i3)                   trigsimp(%)
                       2
                    sin (t)
(%o3)                     -------
                       2
 

OK this works but it seems like a long way around for beginning students.

My real problem was to get Maxima to show all the intermediate steps in 
calculating an answer to a question.
Other people have brought this up in the past and I am not asking that 
it be visited again, I am just explaining why I am doing all this.