Roman,
> (%i25) romberg(exp(-t)/sqrt(1-t*t),t,-1,1);
The romberg and quanc8 numerical integration functions are
superseded by the quadpack functions, which are based on
Gauss-Kronrod rules.
e : exp(-t)/sqrt(1-t*t);
quad_qags (e, t, -1, 1);
=> [3.977463260506118, 4.0535934608953994E-9, 567, 0]
quad_qags (adaptive subdivision, general integrand) doesn't
evaluate the integrand at the endpoints -1 and 1.
I believe this is generally true of Gaussian integration rules.
? quad
should tell about the available quadpack functions.
HTH
Robert Dodier