SI. 3 Given that there are $C$ integers that satisfy the equation $|x-2|+|x+1|=B$, find the value of $C$ Reference: 1994 HG1, 2001 HG9, 2004 FG4.2, 2008 HI8, 2008 FI1.3, 2010 HG6, 2012 FG2.3
$\begin{array}{l}|x-2|+|x+1|=3 \\ \text { If } x<-1,2-x-x-1=3 \Rightarrow x=-1 \text { (rejected) } \\ \text { If }-1 \leq x \leq 2,2-x+x+1=3 \Rightarrow 3=3 \text {, always true }-1 \leq x \leq 2 \\ \text { If } 2<x, x-2+x+1=3 \Rightarrow x=2 \text { (reject) } \\ \quad-1 \leq x \leq 2 \text { only } \\ \because x \text { is an integer, } \quad x=-1,0,1,2 ; C=4\end{array}$