A

Given the function \[ F(x) = \frac{1} {4}x^{4} -\frac{5} {2}x^{2}, \] find the function \(f\) such that \(F\) is primitive to \(f\) on \(\mathbb{R}\).

Given the function \[ F(x) = x + \frac{9} {2}x^{2} + 9x^{3} + \frac{27} {4} x^{4}, \] find the function \(f\) such that \(F\) is primitive to \(f\) on \(\mathbb{R}\).

Given the function \[ F(x) = \frac{6} {7}x^{3}\sqrt{x}, \] find the function \(f\) such that \(F\) is primitive to \(f\) on the interval \((0;+\infty)\).

Find the area of the region bounded by the curves \(y = 0\), \(y = x^{3}\), \(x = 1\) and \(x = 3\).