Get the Integrate[1-Erf[1]^2-E^(-Sec[t]^2),{t,0,Pi/4}] ?

Questions
1

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?

2

NIntegrate is a numerical function. It’s not expected to return an exact answer. Integrate is not able to do all integrals.