A United Airbus A319-100, registration N834UA performing flight UA-1536 from San Francisco,CA to Jackson Hole,WY (USA), was descending towards Jackson when the crew reported an interior fire originating from batteries. The flight crew continued to Jackson and landed the aircraft without further incident while flight attendants extinguished the fire and cooled the batteries. The FAA reported two flight attendants and one passenger received minor injuries when an interior fire from batteries occurred. Flight attendants extinguished the fire. The aircraft did not sustain damage.