Bug introduced in 10.2.0 or earlier and fixed by 11.0.
Integrate[Exp[c x]/x, {x, -a, a}]
returns
ConditionalExpression[-ExpIntegralEi[-a c] + ExpIntegralEi[a c], Re[a] > 0 && Im[a] == 0]
but the integral does not actually converge for any values of c or a (because near x = 0, Exp[c x] ~ 1, so the integrand has a 1/x singularity). If I replace either c or a with an actual number, then Mathematica correctly says that the integral does not converge - even if I replace c with a positive real number, satisfying the returned condition.