Final answer:
Francis Cabot Lowell did initiate the first integrated textile mill in New England with his Boston Manufacturing Company, marking a significant step in the American Industrial Revolution.
Step-by-step explanation:
The statement "Francis Cabot Lowell built the first integrated textile mill in New England" is true. Lowell is particularly known for having revolutionized the American textile industry during the Industrial Revolution in the United States. He established the Boston Manufacturing Company in Waltham, Massachusetts, in 1813, which integrated all the processes of textile production under one roof. This innovation drastically increased efficiency and marked the start of the factory system revolution in America.