i.4.35 Curvilinear integrals

Condition: Calculate the curvilinear integral taken along spatial curves (the coordinate system is assumed to be right-handed): \[ \int_{C}\left(y^{2}-z^{2}\right) d x+2 y z d y-x^{2} d z \] where \( C- \) curve \( x=t, y=t^{2}, z=t^{3}(0 \leq t \leq 1) \), run in the direction of increasing parameter.