Let f(x)=x2+2. A classmate proposes F(x)=3x3+2x as an antiderivative of f(x). Answer the following:
(i) Verify whether F(x) is an antiderivative of f(x).
(ii) Write the most general antiderivative of f(x).
(iii) Find the particular antiderivative that satisfies F(1)=5.