Factual error: The film takes place around 1830, but you can see a character using a Colt Navy 1851, which was made 21 years later actually.
Factual error: The American Flags being flown have the 13 stripes and 50 state stars. This is 1847 so only 29 stars should be shown on the flags.
Answer: It is called "Manifest Destiny" and was done by Michael Nyman and Damon Albarn. It is on the soundtrack.