Final answer:
Francis Cabot Lowell indeed built the first integrated textile mill in New England, which was significant for the American industrial revolution in the textile industry.
Step-by-step explanation:
The statement 'Francis Cabot Lowell built the first integrated textile mill in New England' is true. Lowell was a key figure in the industrial revolution in America, particularly known for his contribution to the textile industry. In the early 19th century, he established the Boston Manufacturing Company in Waltham, Massachusetts, which became the first integrated textile mill in New England, and revolutionized the industry by centralizing the entire production process under one roof.