Men in Black 3

In 2012, an alien criminal, Boris the Animal, a Boglodite, escapes from a maximum-security prison on the moon and arrives on Earth, bent on taking revenge on Agent K, who shot off his left arm and captured him in 1969. He confronts K, who is with his partner Agent J, telling him he is "already dead". J then discovers that K was responsible not only for capturing Boris, but for deploying the "ArcNet", a shield that prevented the Boglodites from conquering Earth and caused their extinction.
Boris travels back in time to kill the young Agent K. With history altered so that K is long-dead, J finds that only his memory has been unaffected, and no one from the Agency understands his obsession with K until Agent O, the new Chief, deduces that there has been a fracture in the space-time continuum. With K out of the picture, the ArcNet was never deployed, and there is nothing to protect the present-day Earth from the Boglodite invasion, so J must travel back in time to stop Boris and save K. Back in 1969, he travels to Coney Island, knowing from the Agency's records that, in 1969, Boris will commit a murder there. He finds Boris, but is discovered and arrested by 1969 K, who prepares to wipe his memory, but decides at the last minute to investigate J's claims. K and J follow clues, leading them to a bowling alley, and then to The Factory, where they come across an alien named Griffin, who is in possession of the ArcNet. Griffin, who can see all possible future timelines and outcomes, senses Boris is coming and escapes, but he later captures him. J and K pursue and rescue Griffin, acquiring the ArcNet. 1969 Boris escapes and 2012 Boris arrives and they team up.
Upon learning that they must go to Cape Canaveral, Florida and attach the ArcNet to the Apollo 11 rocket so it can be deployed in space, J reveals the real purpose of his mission to K, who initially takes the news badly. The three fly there using jetpacks, and are stopped by military police. Griffin shows a skeptical colonel the future, convincing him of the importance of their mission, and the officer then assists them in reaching the launch site. As the agents climb up the rocket's launch tower, they are attacked by both 1969 Boris and 2012 Boris. Using his time-travel device, J evades an attack by 2012 Boris and knocks him off one of the launch tower bridges. K shoots off 1969 Boris's left arm (which restores the timeline), knocking him off the tower as well. The ArcNet is attached and deploys successfully when the rocket launches, with 2012 Boris being incinerated by the rocket's exhaust. 1969 Boris then attacks K on the beach, but the colonel pushes K down and out of the way, taking the hit himself instead. K then kills Boris (which 2012 K had regretted not doing) instead of arresting him as he originally did. The colonel's young son inquires about his father, but rather than tell him the truth, K wipes his memory and tells him only that his father is a hero. Observing from afar, J realizes that the young boy is himself, the colonel was his father, and that K has actually been watching over him all his life. His mission complete, J returns to 2012, where he thanks K for being his surrogate father. Meanwhile, Griffin observes the moment and is briefly terrified when K almost forgets to tip a waitress, which sets off a chain of events preventing an asteroid from colliding with Earth.

Question: What year does J travel back to?
Answer: 1969