Integral of Taylor expansions



Dear list,
   I would like to use Taylor expansions to approximate integrals and
I see the following problem:

this trivial case works as expected, yielding   p(0) l
pT : taylor(p(s),s,0,0);
pT : ratsimp(pT);
pbar : integrate(pT,s,-l/2,l/2);

but when I take
pT : taylor(p(s),s,0,1);
pT : ratsimp(pT);
pbar : integrate(pT,s,-l/2,l/2);
maxima starts computing and never delivers any result. Does anyone
have a suggestion?

Thank you!
   Marco