How to hook up a subwoofer with an integrated amp?

You use the preamp out on the amp to the preamp in on the sub. You can also use speaker out on the amp to the speaker level in on the sub. There are many different options depending on what sub you get. Here is the owners manual of the SVS sub that explains all the options on subwoofer hookup! BTW,what is your budget?
https://system.na1.netsuite.com/core/media/media.nl?id=69175&c=3634088&h=a2a627c5bd0810a8a24...

I was told if I connect to the speaker out on the integrated amp the subwoofer would be controlled  the volume control on the integrated amp. 

Why would you want it any other way? The volume control will also work like that using the preamp outs!

You can set the desired volume and crossover settings on the subwoofer itself and control the overall volume with the volume control of the preamp. You need to experiment with the volume control on the sub to find a position that sounds good to you at all preamp volume levels. As yogi said, use the preamp outs to the subs in with a decent interconnect of the proper length.