Answer
$\int\limits_1^3 (x^{2}+2x-4) dx=\dfrac{26}{3}$
Work Step by Step
$\int\limits_1^3 (x^{2}+2x-4) dx$
Integrate each term:
$\int\limits_1^3 x^{2} dx +\int\limits_1^3 2x dx-\int\limits_1^3 4 dx=...$
Take the constants out of the integral and evaluate each individual integral:
$...=\int\limits_1^3 x^{2} dx+2\int\limits_1^3 x dx-4\int_\limits1^3dx=...$
$...=\dfrac{1}{3}x^{3}+(2)(\dfrac{1}{2})x^{2}-4x\Big|_1^3=...$
$...=\dfrac{1}{3}x^{3}+x^{2}-4x\Big|_1^3=...$
Apply the second part of the fundamental theorem of calculus to get the result:
$...=\Big[\dfrac{1}{3}(3)^{3}+(3)^{2}-4(3)\Big]-\Big[\dfrac{1}{3}(1)^3+(1)^2-4(1)\Big]=...$
$...=\dfrac{1}{3}(27)+9-12-\dfrac{1}{3}-1+4=...$
$...=9+9-12-\dfrac{1}{3}-1+4=\dfrac{26}{3}$
