(Antiderivatives – Constant of Integration)
Answer all parts.
(i) Define an antiderivative (indefinite integral) of a function f(x).
(ii) Explain, with reason, why an arbitrary constant must be added while writing the most general antiderivative of a function.
(iii) If F(x) is any one antiderivative of f(x), show that F(x)+k is also an antiderivative of f(x) for every real constant k.