I want to verify if my result is correct. I need to evaluate this line integral:
$$\int_{C} \bigl( (y^{2}-z^{2}) dx + 2yzdy - x^{2}dz \bigr)$$
where $C$ is defined by: $C:\begin{cases} x=t \\ y=t^{2} \\ z=t^{3} \end{cases}$ between the points $O(0,0,0)$ and $A(1,1,1)$. I got
\begin{align*} &=\int_{0}^{1}y^{2}dx-\int_{0}^{1}z^{2}dx+\int_{0}^{1}2yzdy-\int_{0}^{1}x^{2}dz \\ &=\int_{0}^{1}t^{4}dt-\int_{0}^{1}t^{6}dt+\int_{0}^{1}2t^{5}(2t)dt-\int_{0}^{1}t^{2}(3t^{2})dt \end{align*}
and after calculations I got $\frac{1}{35}$ as result.
Is correct?