Berechne das Wegintegral ${\displaystyle {}\int _{\gamma }\omega }$ zu

${\displaystyle \gamma \colon [-1,0]\longrightarrow \mathbb {R} ^{3},\,t\longmapsto (-t^{2},t^{3}-1,t+2),}$

für die ${\displaystyle {}1}$-Differentialform

${\displaystyle \omega =x^{3}dx-yzdy+xz^{2}dz}$

${\displaystyle {}\mathbb {R} ^{3}}$