You can get full credit for this problem by just answering the last question correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. The integral

$\displaystyle \(\displaystyle \int_{-1}^{6}\left|12 x^2 - x^3 - 32 x\right|\, dx\)$ MUST be evaluated by breaking it up into a sum of three integrals:

$\displaystyle \[\int_{-1}^a\left|12 x^2 - x^3 - 32 x\right|\, dx +\] \[\int_a^c\left|12 x^2 - x^3 - 32 x\right|\, dx +\] \[\int_c^{6}\left|12 x^2 - x^3 - 32 x\right|\, dx\] $where

$\displaystyle a =$

$\displaystyle c =$

$\displaystyle \(\displaystyle \int_{-1}^a\left|12 x^2 - x^3 - 32 x\right|\, dx\) =$

$\displaystyle \(\displaystyle \int_a^c\left|12 x^2 - x^3 - 32 x\right|\, dx\) =$

$\displaystyle \(\displaystyle \int_c^{6}\left|12 x^2 - x^3 - 32 x\right|\, dx\)=$

Thus

$\displaystyle \(\displaystyle \int_{-1}^{6}\left|12 x^2 - x^3 - 32 x\right|\, dx\)=$

**Note: ***You can earn full credit by answering just the last part.*