Answer the following questions related to indefinite integrals and the constant of integration.
a. (i) State the definition of an indefinite integral of a function f in terms of its antiderivative.
b. (ii) Explain, without performing any calculation, why every antiderivative of a given function must include an arbitrary constant.
c. (iii) Using your explanation in part (ii), describe how any two antiderivatives of the same function are related.