Final answer:
The first cotton mill in England opened in 1764 and was associated with the invention of the water frame by Richard Arkwright. America's first textile mill was built by Samuel Slater in the 1790s in Pawtucket, Rhode Island. The first integrated textile mill in America was established by Francis Cabot Lowell in 1814 in Waltham, Massachusetts.
Step-by-step explanation:
The first cotton mill in England was established in the year 1764. This textile mill marked the beginning of a more industrialized approach to cotton fabric production. Before this, the majority of England's cloth was made from wool, with cotton requiring more processing. The establishment of the mill coincided with Richard Arkwright's invention of the water frame in 1769, which was later housed in his mill in 1771. This machine used waterpower to spin cotton into thread and represented a significant development in the history of manufacturing.
In America, Samuel Slater, often known as the 'Father of the American Industrial Revolution', built the first American textile mill in Pawtucket, Rhode Island, in the 1790s with the aid of merchant Moses Brown. Slater's operation similarly utilized waterpower to British mills, but it was his creation of the first mill village, Slatersville, that integrated the elements of a factory, housing, and a company store. By 1809, the northeastern part of the United States would see a proliferation of mills, with eighty-seven spinning mills in operation.
It was not until Francis Cabot Lowell established the Boston Manufacturing Company in 1814, at Waltham, Massachusetts, that the United States would see its first integrated mill. This mill incorporated all stages of cotton fabric production within a single building and became a model for future American industrial enterprises in the textile industry.