Jeff's got the right idea.
"Integrated Motion", in the Rockwell Automation world, is the control of motion axes using the ControlLogix motion control architecture with Motion modules (1756-M02AE, M02SE, -HYD02), SERCOS-connected drives, or drives connected over EtherNet/IP using the CIP Motion protocol.
The ControlLogix motion architecture means you're using Axis objects, and using the built-in Motion instruction set in RSLogix 5000. This includes CompactLogix controllers that include motion functionality.
Examples:
A control system using a 1769-L18ER controller and Kinetix 300 drives treats the drives like I/O objects, and sends them index positions and start/stop/reset commands over an ordinary I/O connection. This is a "discrete motion" or "non-integrated motion" system.
A control system using a 1769-L18ERM controller and Kinetix 350 drives uses the CIP Motion protocol over Ethernet, and the drives are represented as Axis objects in the RSLogix 5000 project tree. The controller uses Logix 5000 motion instructions (Motion Servo On, Motion Axis Move, Motion Axis Stop, Motion Axis Gear, etc) to control the servomotors.
Now ask me about the differences between Simotion, Simatic, and Sinamics. I'll get it straight eventually, but having multiple technologies "integrated" inside a controller that takes five steps to perform a download takes some getting used to.