entomology - Do ants really dispose of their own dead, and how/why?

I just read this from Wikipedia's Swarm Behavior article:

Despite the lack of centralized decision making, ant colonies exhibit complex behaviour and have even been able to demonstrate the ability to solve geometric problems. For example, colonies routinely find the maximum distance from all colony entrances to dispose of dead bodies.

There was no citation.

Is it true that ants dispose of their own dead? If so, how and why? I would've though it would be much better to just eat their own dead, which would be a "free" food source allowing the colony to reclaim some protein and nutrients. It would cost much more energy (and risk) to transport dead ant carcasses away from the hive.