Usually, "subwoofer to satellite integration" refers to the cross-over region between the sub and the satellite speakers.
The cross-over is not a "brick wall". It's not as though the subwoofer plays all the frequencies up to an including 80Hz and then completely stops making any sounds above that frequency. And the speakers don't just go from 20,000 Hz down to 80Hz and stop completely below that.
Rather, the higher frequencies from the subwoofer get gradually quieter and quieter and the lower frequencies from the speakers get quieter and quieter. Just how steep the slopes are is decided by the design of the cross-over circuitry.
So sometimes, the speakers will naturally start to roll-off their bass output too soon or have a built-in slope that is very steep. Or perhaps the subwoofer starts to roll-off its higher frequencies too soon or also has a built-in slope that is too steep. If that's the case, you could end up with a "hole" in the frequency response where the low end of the speakers doesn't mesh nicely with the higher end of the subwoofer.
On the other end of the spectrum, if the speakers reach down very low before they roll-off at all and the subwoofer reaches up fairly high before rolling-off, you end up with that cross-over range being too loud and you have a "hump" in the frequency response.
So one, very well known cross-over design is the THX standard cross-over. With a THX cross-over, 4th order slopes are used - which are quite steep: 24dB per octave. The subwoofer should play completely flat from 20Hz up to about 70Hz. Starting at about 70Hz, the subwoofer should start to roll-off so that it is 3 dB quieter at 80Hz and at 160Hz, it should be 24 dB quieter still. The speakers should be flat from 20,000 Hz all the way down to about 90 Hz. At 90Hz, they start to roll off so that at 80Hz, they too are 3 dB quieter. And at 40Hz, they would be 24dB quieter still.
The thing is, the speakers themselves will naturally start to roll-off at some point. A THX speaker is specifically designed to have a 2nd order (12dB/octave) natural roll off starting at about 90Hz so that the speaker, on its own, is 3dB quieter at 80Hz. The real magic of the THX cross-over happens inside the THX processor or THX receiver. The THX subwoofer, completely on its own, should be able to play flat all the way up to 160Hz. The THX processor/receiver will apply the complete 4th order slope to the subwoofer. For the speakers, the THX processor/receiver will apply a 2nd order slope. The natural 2nd order slope of the speakers themselves cascades with the 2nd order slope applied by the processor to create a 4th order slope! Pretty smart
End result - the entire frequency range from 20Hz up to 20,000 Hz is flat and linear. There is no "hole" in the frequency response where the subwoofer and the speakers cross over; and there is no "hump" either. The steep 4th order slopes ensure that virtually all of the bass comes from the subwoofer and also that the subwoofer produces very little in the way of higher frequencies. This keeps the bass difficult to localize and it allows the speakers to be physically smaller and to demand less power because they do not have to try and produce much at all in the way of bass frequencies.