$If{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}f(x)dx=\frac{2}{5}{x}^5-\frac{1}{3}{x}^2+C,$ then determine a formula for $f(x)$

$(A)\frac{2}{25}{x}^6-\frac{1}{6}{x}^3+C$

$(B)2x^4-\frac{2}{3}x$

$(C)\frac{8}{5}{x}^4-\frac{1}{3}x+C$

$(D)\frac{1}{15}{x}^6-\frac{1}{9}{x}^3+C$

$(E)\frac{1}{15}{x}^6-\frac{1}{9}{x}^3$