Trigonometric definite integral resulting in sinc-likefunction

On Sat, 17 Jul 2010, Stavros Macrakis wrote:

> Maxima makes many simplifications which assume non-singular cases, for
> example x/x=>1.  This is actually a perfectly reasonable thing to do, for
> two reasons:

...

> Rather than say that the result of integrate(cos(a*x),x) should be (if a=0
> then x else sin(a*x)/a), I would prefer to say that the Maxima
> expression sin(a*x)/a denotes the function defined by that expression when
> a<>0 and its analytical continuation when a=0.

I agree with this, but I will plead that this is not really about the
handling of singularities.  m = 0 is an ordinary point of both
sin(2*%pi*m)/m and m/sin(2*%pi*m).  But subst(m = 0,...) artificially
introduces a singularity in the former, and declare(m,integer)
artificially introduces a singularity in the latter.

-- 

Regards,

Dan