Находим первообразную:

[tex] \displaystyle F(x) = \int( {4x}^{5} - 5x)dx = \not4 \int \bigg(\frac{ {x}^{6} }{ \not6} - \frac{5}{2} {x}^{2} \bigg)dx = \\ [/tex]

[tex] \displaystyle = \frac{2}{3} {x}^{6} - \frac{5}{2} {x}^{2} + C[/tex]

F(x) = -2; x = 1

[tex] \displaystyle\frac{2}{3} \: * \: {1}^{6} - \frac{5}{2} \: * \: {1}^{2} + C = - 2[/tex]

[tex] \displaystyle \frac{\stackrel{2/}{}2}{3} - \frac{\stackrel{3/}{}5}{2} + C = - 2[/tex]

[tex] \displaystyle - \frac{11}{6} + C = - 2[/tex]

[tex] \displaystyle C = \stackrel{3/}{} -2 + \frac{11}{6} [/tex]

[tex] \displaystyle C = \frac{5}{6} [/tex]

[tex] \displaystyle \boldsymbol F(x) = \frac{2}{3} {x}^{6} - \frac{5}{2} {x}^{2} + \frac{5}{6} [/tex]