Final answer:
Hawaii was not brought under the American flag by the Spanish-American War; it was annexed prior to the war. Puerto Rico, Guam, and the Philippines were ceded to the United States following the war's conclusion, with Cuba gaining nominal independence but remaining under U.S. influence.
Step-by-step explanation:
The territories that were not brought under the American flag by the Spanish-American War include Hawaii (c). After the conclusion of the war, the United States acquired Puerto Rico, Guam, and the Philippines. While all were previously Spanish colonies, Hawaii was annexed by the United States as a result of a separate process prior to the war.
After the war, the Treaty of Paris was signed in December 1898, leading to Spain recognizing Cuba's independence and ceding Guam and Puerto Rico to the United States, along with allowing the United States to purchase the Philippines. Although Cuba gained independence, it remained under strong U.S. influence due to various interventions and amendments like the Platt Amendment that affected its sovereignty.
Hawaii's inclusion in the United States occurred as a result of its annexation in 1898, but this was not a direct outcome of the Spanish-American War. Instead, Hawaii's strategic location and the interests of American planters played a significant role in its annexation.