Sage's symbolic integration is currently just calling out to Maxima,
so you might ask about this on a Maxima list. Maxima's symbolic
integration is some huge undocumented lisp program from ages gone
by...
The above doesn't return a closed result partly because Maxima doesn't:
wstein@sage:~$ sage -maxima
Maxima 5.23.2 http://maxima.sourceforge.net
(%i1) integrate(abs(x^2-1),x,-2,2)
;
2
/
[ ! 2 !
(%o1) I !x - 1! dx
]
/
- 2
You might find this useful though:
sage: numerical_integral(abs(x^2-1),-2,2)
(3.9999999999999996, 4.4408920985006262e-14)
or
sage: N(integral(abs(x^2-1),(x,-2,2)))
3.9999999999999996
> How can one cooperate without being a sage programmer?
>
> Thank you.
>
> Pedro
>
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--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org