Agroup of people that share a distinctive race, culture, heritage, or nationality is a(n):
discrimination
integration
segregation
race
ethnic group

The words "discrimination", "segregation" and "integration" refer to the group interaction between the majority and minority - integration suggests a positive interaction and the other two a negative one. But they don't describe a group, so they can't be a correct answer.

The correct answer is "ethnic group" - it's more than race since culture is also shared!