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Solution:

sub intervals: [0,1] , [1,2] , [n-1,1]

each sub interval has base 1 and height 1, 2 , .... n respectively....

Thus: ∫ [t] dt = Ʃ [t](base) from i = 1 to n = n is base(=1)(1 + 2 + .... + n)

= 1 + 2 + .... n =/= n(n-1)/2

some help please...?