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.