Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2016 / Paper 1 / 7 / b

Additivity of the definite integral combines the adjacent intervals into $[0,n]$. For an integer $n\ge 1$, the power rule givesFor $n=0$, interpret the indexed sum as an empty sum, equal to zero; the displayed expression also gives zero. This convention resolves the otherwise degenerate endpoint of the stated nonnegative-integer range.