I.4.35 Curvilinear Integrals

Condition: Calculate the curved integral taken along the spatial curves (the coordinate system is supposed to be right): \ [\ int_ {c} \ left (y^{2} -z^{2} \ right) d x+2 y z d y-x^{2} d z \] where \ (c- (c- c- (C- \) Curve \ (x = t, y = t^{2}, z = t^{3} (0 \ leq t \ leq 1) \) running in the direction of the parameter increase.