From 0 to 1 again

Let $u=x+2$ . Now we have $(u-2)u^4 \times \frac{dx}{du} = (u^5 - 2u^4) \times 1$ which upon integration gives us $\frac{u^6}{6} - \frac{2u^5}{5}$ . Now the limits need to be changed from 0 to 1 to 2 to 3. Your final answer should be $\frac{3^6-2^6}{6} - \frac{2(3^5-2^5)}{5}$ = $\frac{665}{6} - \frac{422}{5} = \frac{793}{30}$ . So $a+b = 793+30= \boxed{823}$