Let f : R → R be defined by <span class="math-tex">\(\rm f(x)=\left\{\begin{matrix} \rm x+2 &\rm if\ x<0 \\ \rm |x-2| &\rm if \ x\geq0 \end{matrix}\right.\)</span>. Find <span class="math-tex">\(\rm \int_{-2}^{\ \ 3} f(x)\ dx\)</span>.
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