A liitle help with a concept?

Hi All,

I am trying to use maxima to manipulate sum infinite
sums.  I am having a few problems but they all relate
to the small example below.  This command 

(C4) integrate(sum(sin(n*%PI*e/l),n,1,INF),e,0,l);

Has the results

(D4)
l*('LIMIT('SUM(COS(%PI*e*n/l)/n,n,1,INF),e,0,PLUS))/%PI
     
-l*('LIMIT('SUM(COS(%PI*e*n/l)/n,n,1,INF),e,l,MINUS))/%PI

yet a can (on paper) take the integral inside the sum
and integrate term by term to get:

(C5) integrate(sin(n*%PI*e/l),e,0,l);

(D5) l/(%PI*n)-l*COS(%PI*n)/(%PI*n)

The result is correct in D4 so my question is how do
get get maxima to evaluate the limit?

Thanks
Kevin