There are sites that test the power consumption at the wall based on various configurations. Some use integrated graphics, others use a dedicated graphics card and they state which card they use. It's not cpu only power, rather system idle so includes the small amount of power consumed by a hard drive and motherboard. The more devices connected the more power will be consumed.
These are a few power consumption tests.
http://www.anandtech.com/show/8774/intel-haswell-low-power-cpu-review-core-i3-4130t-i5-4570s-and-i7-4790s-tested
http://www.anandtech.com/show/7963/the-intel-haswell-refresh-review-core-i7-4790-i5-4690-and-i3-4360-tested/2
http://www.xbitlabs.com/articles/cpu/display/intel-haswell-refresh_6.html
It will also vary slightly whether you choose to use haswell's c6/c7 extreme low power sleep states (and whether the power supply can handle those extended sleep states) as well as how you set up your power plan if using windows. For instance whether you set the power plan to performance, balanced, power saver or set custom settings for how long before the monitor powers down, hard disks etc.
Integrated graphics should idle when the cpu does and likely won't take much power when the monitor goes off (sleep mode). Just a fraction of the power as when it's being used and if it's a media server then chances are you won't be using it a whole lot other than setting things up or maintaining it. You could turn the monitor off and the igpu should idle with no video output reducing what little power it consumes and heat as well.
No worries, you weren't wrong exactly. Motherboards did used to have onboard graphics and the ones that did had a video port on the back. Otherwise people used the video port on the graphics card for their monitor. So yes, that was a thing. Some amd cpu's (called apu's) have integrated graphics. Intel has integrated graphics in nearly all their recent cpu's and instead calls it an igpu (integrated graphics processing unit). When you look at the metal cover on a cpu like the i5 4590, underneath it are not only the 4 cpu cores but also a graphics card (albeit a very small one).
The only thing is since the integrated graphics don't have a large board like a video card does, there's no room for its own video ram so has to borrow from the system memory. Same as older video chips integrated to the motherboard.