$800-$1500 Integrated amps with a subwoofer output

Agree with seandtaylor99. I currently run a REL Strata with my Sonus Fabers using a VAC tube integrated amp with great results.

Sounds like you are looking for a specific subwoofer output that usually comes with a receiver for home theater. For two channel, there are similar threads out to look at different hook ups. Personally, I don't think a specific sub out is necessary.

Suits-me makes a very good observation. Running a long set of interconnects from a passive preamp can audibly affect the frequency response (due to cable capacitance), so it would be better to get an integrated with an active preamp if you want to use RCA interconnects to drive the sub. Unfortunately, since the demise of phono inputs many integrateds have a passive-pre.
Or just get a REL / ACI sub and connect to the speaker terminals.

Antique Sound Lab offers integrated tube amps in the low to mid range of that price range that have RCA sub outs. I have the 1003, and the sub outs were a definite advantage that some of the comparables did not have.

I second Antique Sound Labs. I think nearly all their new models have sub out but if you buy used, ask about it first because the early amps didn't.