Remove some questions in trig integration



There is a thread at the sage-support forum about questions asked when
integrating trig functions:

http://groups.google.com/group/sage-support/browse_frm/thread/c60c50a50c3b6ea5#

It is about questions in the integrations

(%i1) integrate(sec(t)*tan(t),t,0,%pi/3);
Is  cos(t)  positive, negative, or zero?pos;
(%o1) 1
(%i2) integrate(csc(x)*cot(x),x,%pi/3,%pi/2);
Is  sin(x)  positive, negative, or zero?pos;
Is  sin(x+%pi/3)  positive, negative, or zero?pos;
(%o2) 2/sqrt(3)-1

The questions come from sin-cos-intsubs1 in src/defint.lisp:

(defun sin-cos-intsubs1 (exp)
  (let* ((rat-exp ($rat exp))
	 (num (pdis (cadr rat-exp)))
	 (denom (pdis (cddr rat-exp))))
    (cond ((not (equal (intsubs num ll ul) 0.))
	   (intsubs exp ll ul))
	  ;; Why do we want to return zero when the denom is not zero?
	  ;; That doesn't seem to make sense to me (rtoy).  Checking
	  ;; for a zero denominator makes sense, but what we should
	  ;; return in that case?  0 seems like a bad choice.  $inf or
	  ;; $undefined seem like better choices.  Or maybe just
	  ;; signaling an error?
	  #+nil
	  ((not (equal ($asksign denom) '$zero))
	   0)
	  ((equal ($asksign denom) '$zero)
	   '$undefined)
	  (t (intsubs exp ll ul)))))

sin-cos-intsubs1 substitutes the limits of integration into the
antiderivative. If the antiderivative is f(x)/g(x) and f(ll)=f(ul) it
does a special check to see if the denominator is zero and returns
undefined if it is.

I think there is no real reason for this check, so I propose we remove
it. Or at least change $asksign to csign.

Andrej