Answer
$$\frac{{965}}{6}$$
Work Step by Step
$$\eqalign{
& \int_1^6 {\left( {2{x^2} + x} \right)} dx \cr
& {\text{integrate by using }}\int {{x^n}} dx = \frac{{{x^{n + 1}}}}{{n + 1}} + C{\text{ and }}\int {dx} = x + C \cr
& = \left( {2\left( {\frac{{{x^{2 + 1}}}}{{2 + 1}}} \right) + \frac{{{x^{1 + 1}}}}{{1 + 1}}} \right)_1^2 \cr
& = \left( {\frac{2}{3}{x^3} + \frac{{{x^2}}}{2}} \right)_1^2 \cr
& {\text{use fundamental theorem of calculus }}\int_a^b {f\left( x \right)} dx = F\left( b \right) - F\left( a \right).\,\,\,\,\left( {{\text{see page 388}}} \right) \cr
& = \left( {\frac{2}{3}{{\left( 2 \right)}^3} + \frac{{{{\left( 2 \right)}^2}}}{2}} \right) - \left( {\frac{2}{3}{{\left( 1 \right)}^3} + \frac{{{{\left( 1 \right)}^2}}}{2}} \right) \cr
& {\text{simplifying}} \cr
& = \left( {144 + 18} \right) - \left( {\frac{2}{3} + \frac{1}{2}} \right) \cr
& = 162 - \frac{7}{6} \cr
& = \frac{{965}}{6} \cr} $$
