Answer:
The sentence would be as follows: Baseball has been a part of America's history for hundreds of years.
Step-by-step explanation:
In the sentence above, you should indicate possession between the noun America and the noun history because the speaker is referring to the history of America. In order to show possession with a singular noun, you should add an apostrophe plus the letter -s. Therefore, if you are to indicate possession with the singular noun America, you should add the apostrophe plus the -s (America's).