The antiderivative for sin(x)/x is fine, except that using it naively for definite integrals is not.
(%i5) eq:sin(x)/x;
sin(x)
(%o5) ------
x
(%i6) integrate(eq, x, -1e-6, 1e-6);
rat: replaced 2.0e-6 by 1/500000 = 2.0e-6
snip
rat: replaced 10.0e-7 by 1/1000000 = 10.0e-7
%i %i
(%o6) %i gamma_incomplete(0, - -------) - %i gamma_incomplete(0, -------)
1000000 1000000
(%i7) fullmap('float,%);
(%o7) %i (1.570795326794897 %i + 13.23829489306299)
- (13.23829489306299 - 1.570795326794897 %i) %i
which I believe is -pi, which also happens upstream at http://trac.sagemath.org/ticket/11164 because we use the same branch cuts for this.
gamma_expand just causes a different problem.
(%i10) integrate(eq, x, -1e-6, 1e-6), gamma_expand:true;
rat: replaced 2.0e-6 by 1/500000 = 2.0e-6
...
(%o10) 3.141594653589793
