The correct answer is C. III
The territory shown in territory III is known as the Mexican Cession. This piece of land was given to the United States in the Treaty of Guadalupe Hidalgo. This treaty officially ended the Mexican American War.
This territory includes modern day California, Arizona, New Mexico, Utah, Colorado, and parts of Wyoming. This treaty negatively impacted Mexico, as they lost nearly 1/3rd of their land to the United States.