Answer
\[\frac{{212}}{5}\]
Work Step by Step
\[\begin{gathered}
\int_{ - 2}^2 {\,\left( {3{x^4} - 2x + 1} \right)dx} \hfill \\
\hfill \\
integrate\,\,\int {{x^n}dx = \frac{{{x^{n + 1}}}}{{n + 1}} + C} \hfill \\
\hfill \\
\,\,\left[ {\frac{{3{x^5}}}{5} - {x^2} + x} \right]_{ - 2}^2 \hfill \\
\hfill \\
apply\,\,Fundamental\,\,theorem\,\,of\,\,calculus\,\,,\,therefore \hfill \\
\hfill \\
\,\,\left[ {\frac{{3\,{{\left( 2 \right)}^5}}}{5} - \,{{\left( 2 \right)}^2} + 2} \right] - \,\,\left[ {\frac{{3\,{{\left( { - 2} \right)}^5}}}{5} - \,\,\,{{\left( { - 2} \right)}^2} + 2} \right] \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
\left[ {\frac{{86}}{5}} \right] - \,\,\left[ { - \frac{{126}}{5}} \right] \hfill \\
\hfill \\
\frac{{212}}{5} \hfill \\
\end{gathered} \]
