Let g(x)=3x2−4x+1 for all real x.
(a) Determine the most general antiderivative G(x) of g(x). Show your work.
(b) The graph of G passes through the point (2,5). Find the particular antiderivative that meets this requirement and state its equation.
(c) Differentiate your answer from part (b) to confirm that it indeed yields g(x). Provide a one–sentence conclusion summarizing your check.