부정적분

$f \left( x \right)$$\displaystyle = \int _{} ^{} f' \left( x \right) dx$$\displaystyle = \int _{} ^{} \left( x ^{3} + x \right) dx$ $\displaystyle = \frac{1}{4} x ^{4} + \frac{1}{2} x ^{2} + C \left( C \right.$는 적분상수$\left. \right)$ $C = f \left( 0 \right) = - 1$이므로 $\displaystyle f \left( x \right) = \frac{1}{4} x ^{4} + \frac{1}{2} x ^{2} - 1$ 따라서 $\displaystyle f \left( 2 \right) = \frac{1}{4} \times 2 ^{4} + \frac{1}{2} \times 2 ^{2} - 1 = 5$