Answer
$\displaystyle\int\limits_0^1(u+2)(u-3)du=-\dfrac{37}{6}$
Work Step by Step
$\displaystyle\int\limits_0^1(u+2)(u-3)du$
Evaluate the product present in the integral:
$\displaystyle\int\limits_0^1(u^{2}-3u+2u-6)du=\displaystyle\int\limits_0^1(u^{2}-u-6)du=...$
Integrate each term separately and apply the second part of the fundamental theorem of calculus:
$\displaystyle\int\limits_0^1u^{2}du-\int\limits_0^1udu-6\int\limits_0^1du=\dfrac{1}{3}u^{3}-\dfrac{1}{2}u^{2}-6u\Big|_0^1=...$
$...=\Big[\dfrac{1}{3}(1)^{3}-\dfrac{1}{2}(1)^{2}-6(1)\Big]-\Big[\dfrac{1}{3}(0)^{3}-\dfrac{1}{2}(0)^{2}-6(0)\Big]=...$
$...=\dfrac{1}{3}-\dfrac{1}{2}-6=-\dfrac{37}{6}$
