Actually the 1st generation of the Acura Integra was from 1986 to 1989 and was available as a 2 door and 4 door hatchback. The 2nd generation was from 1990 to 1993 and was available as a 2 door hatchback and a sedan. The third generation was from 1994 to 2001 and also had hatchback and sedan selections. All generations of the Intergra are on the Honda Civic chassis. The fourth generation Integra is marketed as the RSX in the United States and is available only in hatchback form. Everywhere around the world it is still known as the Integra. Acura is to market a 4-door version of the RSX as the Acura TSX except it will be based on the European Honda Accord platform.
The name Integra seems to come from the word integral, meaning 'essential for completeness' or 'possessing everything essential'. Not a bad name for such a car.