2. The number of all integers that satisfy the system of inequalities
$$
\left\{\begin{array}{l}
\frac{2 x-1}{3}+1 \geqslant x-\frac{5-3 x}{2} \\
\frac{x}{5}<3+\frac{x-1}{3}
\end{array}\right.
$$

is ( ).
(A) 1
(B) 2
(C) 21
(D) 22
2.C.

Solve the inequality $\frac{2 x-1}{3}+1 \geqslant x-\frac{5-3 x}{2}$, we get $x \leqslant \frac{19}{11}$.
Solve the inequality $\frac{x}{5}-20$.
Therefore, the solution set of the original system of inequalities is $-20<x \leqslant \frac{19}{11}$. Then all integers that satisfy the original system of inequalities are $-19,-18,-17, \cdots$, $-1,0,1$. A total of 21.