Temporal integration was the process of taking versions of the same individual from two or more different time periods and/or timelines and integrating them into a single person.
Lieutenant Juel Ducane, a 29th century century Starfleet officer who served as the first officer of the Federation timeship Relativity, told Captain Kathryn Janeway and Seven of Nine that the version of Captain Braxton from before he had succumbed to temporal psychosis would be temporally integrated with two other versions of him, both of which were from a point in the future after which Braxton had succumbed to temporal psychosis, so that Braxton could stand trial.
Seven's various trips through time on that occasion resulted in two versions of her existing aboard the USS Voyager in 2375. Ducane assured Captain Janeway that the two Sevens would eventually be integrated as well. (VOY episode: "Relativity")
On December 4, 2381, Commander Ducane stopped a retroassassination attempt on Federation President Nanietta Bacco in Château Thelian, the President's official residence in the Loire Valley in France. He recruited three different versions of Bacco herself to assist him. While one of the three was killed in the attempt, the other two survived and eventually underwent temporal integration. After the process was completed, Bacco retained both sets of memories. (DTI novel: Watching the Clock)
The technique was pioneered by Commander Spock, the first officer and science officer of the USS Enterprise, when the ship was accidentally been sent back in time to Earth in 1969 following its encounter with a Black Star. Spock and Chief Engineer Montgomery Scott determined that they could recreate the time warp which sent the Enterprise back in time via a slingshot effect around the Sun, returning them to their own time of 2267. As they gathered speed around the Sun, they would initially travel back in time and would simply beam US Air Force Captain John Christopher to a point in time before he had been transported aboard the Enterprise. Their plan worked and Christopher was returning to the cockpit of his jet before he had beamed aboard, leaving him with no memory of his encounter with the 23rd century Starfleet crew. (TOS episode: "Tomorrow is Yesterday") As it had been subsequently classified by Starfleet, Ducane had been unaware of this innovation on Spock's part until being informed of it by Shelan, a Suliban agent of the Federation Department of Temporal Investigations in the late 24th century. Ducane informed Shelan that, once he had returned to the 29th century, it would update the historical record accordingly. (DTI novel: Watching the Clock)
By the 31st century, Federation temporal agents had the ability to undergo integration with another version of themselves automatically when they made physical contact, as Jena Noi demonstrated in February 2382. However, the same technology could not be utilised to integrate different versions of other individuals as Noi told Marion Dulmur, another 24th century DTI agent, that she could not replicate the process with the three separate versions of Ducane then in existence without the use of other equipment. (DTI novel: Watching the Clock)