Write the definite integral for the summation: the limit as n goes to infinity of the summation from k equals 1 to n of the product of the square of the quantity 1 plus k over n squared and 1 over n.
the integral from x equals 0 to 1 of x squared, dx
the integral from x equals 1 to 2 of the quantity x plus 1 squared, dx
the integral from x equals 1 to 2 of x squared, dx
the integral from x equals 2 to 1 of x squared, dx