Consider the following code:
Integrate[1-Erf[1]^2-E^(-Sec[t]^2),{t,0,Pi/4}]
returns itself and N[...] returns -7.730361489821647*^-17, while it's actually zero as can be proved. Will WolframAlpha and Machematica support such kind of thing?
NIntegrate is a numerical function. It's not expected to return an exact answer. Integrate is not able to do all integrals.