Is it true that is st. croix part of the us virgin islands based on the following text?

Saint Croix (/sent kr/; Spanish: Santa Cruz; Dutch: Sint-Kruis; French: Sainte-Croix; Danish and Norwegian: Sankt Croix, Taino: Ay Ay) is an island in the Caribbean Sea, and a county and constituent district of the United States Virgin Islands (USVI), an unincorporated territory of the United States.
yes