Title: Higher order corrected trapezoidal rules in Lebesgue and Alexiewicz spaces
Abstract: If f :[a,b] → R such that f (n) is integrable then integration by parts gives the formula ∫ b a f (x)dx = (−1)n n! n−1 ∑ k=0 (−1)n−k−1 [ φ (n−k−1) n (a) f (k)(a)−φ (n−k−1) n (b) f (k)(b) ] +En( f ), where φn is a monic polynomial of degree n and the error is given by En( f ) = (−1)n n! ∫ b