A factory selling chocolates has a marginal cost function $C(x)=0\mathrm{.}01x^2-3x+229,$ where $2$ points $x$ represents the number of chocolates, and a marginal revenue function $R(x)=229-2x.$ Which of the following option$($s$)$ is $($are$)$ correct?

The total profit obtained by the selling $100$ chocolates is $0.$

The total profit obtained by the selling $100$ chocolates is $\frac{5000}{3}.$

The area enclosed by the graphs of the functions $f(x)$ and $g(x)$ is the total profit obtained by selling the first $100$ chocolates.

The area enclosed by the graphs of the functions $f(x)$ and $g(x)$ is the total revenue generated by selling the first $100$ chocolates.