Let f(x)=4x5−3x−2+7x. Answer the following:
a. (i) Find the most general antiderivative F(x) of f(x), writing your answer in the simplest algebraic form.
b. (ii) Differentiate the function obtained in part (i) and show that dxdF(x)=f(x).
c. (iii) If the particular antiderivative satisfies F(1)=10, determine the corresponding value of the constant of integration.