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Scott Design, Inc. What material is the top and what do you mean by "integrated"?

onthefence Stainless counters/integrated sinks are available.

onthefence An ideabook that discusses integrated sinks:

Twisted Minds Custom Designs You can accomplish an integrated sink when using concrete for your sink/countertop. I've included a link to some FAQ's regarding concrete countertops. Please read and decide if concrete is a choice you may want to pursue. If you have any follow up questions, feel free to ask and I'd be happy to answer, or find a local concrete artisan and see what they can offer you.

http://www.houzz.com/discussions/346684/Concrete-Countertops-FAQ-s-by-Twisted-Minds

joyceoliver I haven't picked a counter top yet and by integrated, I mean one piece, like how a Corian sink is integrated into the counter top.

Scott Design, Inc. Kohler manufactures a few tile-in sinks in enamel cast iron. A stone countertop fabricator can use the template provided by Kohler to cut the stone in the size and shape needed. The sink is then placed down inside the cutout resting on shims supported by a sub-surface to make it level with the top of the stone counter leaving a small joint for flexible caulk. The instructions are with the Kohler sinks. My fabricator has done this many times.

Granted there is a seam but you can wipe crumbs, etc. into the sink without interruption and there are no undermount issues. The sinks come in several colors

joyceoliver Excellent suggestion, Scott Design. I will look into it.