The slope field of ${\displaystyle {\frac {dy}{dx}}=x^{2}-x-2}$, with the blue, red, and turquoise lines being ${\displaystyle {\frac {x^{3}}{3}}-{\frac {x^{2}}{2}}-2x+4}$, ${\displaystyle {\frac {x^{3}}{3}}-{\frac {x^{2}}{2}}-2x}$, and ${\displaystyle {\frac {x^{3}}{3}}-{\frac {x^{2}}{2}}-2x-4}$, respectively.