Let∫ be a polynomial of positive degree over an integral domain D.

(a) If char D = 0, then ∫' ≠ 0.

(b) If char D = p ≠ 0, then ∫' = 0 if and only if /is a polynomial in x^P (that is, ∫ = a₀ + a_pX^P + a_2px^2P + • • • +a_ipx^iP).