6. Let $R$ be the region enclosed by $y=x$, $y=x-2$, $y=1$ and $y=0$.

(a) $(10\%)$ Let $A$ be the area of $R$. $A=\underline{\quad(9)\quad}$.

(b) $(5\%)$ The double integral $\iint_R \sqrt{x-y}\,\mathrm{d}x\mathrm{d}y=\underline{\quad(10)\quad}$.