AMC 12 2019b Problem 8

Let $f(x) = x^{2}(1-x)^{2}$. What is the value of the sum

$$f \left(\frac{1}{2019} \right)-f \left(\frac{2}{2019} \right)+f \left(\frac{3}{2019} \right)-f \left(\frac{4}{2019} \right)+\cdots + f \left(\frac{2017}{2019} \right) - f \left(\frac{2018}{2019} \right)?$$

$\textbf{(A) }0 \textbf{(B) }\frac{1}{2019^{4}} \textbf{(C) }\frac{2018^{2}}{2019^{4}} \textbf{(D) }\frac{2020^{2}}{2019^{4}} \textbf{(E) }1$