integral should not be zero

savecancel

Indeed.

sage: F.nintegrate(x,0,2*pi)
(8.0, 8.881784197001255e-14, 21, 0)

Maxima does this correctly internally.

(%i2) integrate( sqrt((cos(x) - 1)^2 + sin(x)^2), x, 0, 2*%pi);
(%o2)                                  8

But

(%i5) load(abs_integrate);
(%o5) /Users/.../sage/local/share/maxima/5.34.1/share/contr\
ib/integration/abs_integrate.mac
(%i6) integrate( sqrt((cos(x) - 1)^2 + sin(x)^2), x, 0, 2*%pi);
(%o6)                                  0

So this seems to be a bug in that package.