Given $f(x)=x^3-6x^{2}4x-3,$ determine which of the following would correctly describe its antiderivative, $F(x).$

$F(x)=3x^2-12x4$

$F(x)=\frac{1}{4}{x}^4-2x^{3}2x^2-3x$

$F(x)=\frac{1}{4}{x}^4-2x^{3}2x^{2}C$

$F(x)=\frac{1}{4}{x}^4-2x^{3}2x^2-3xC$

$F(x)=4x^4-18x^{3}8x^2-3xC$