Compute \(\int_{C} \mathbf{F} \cdot d \mathbf{r}\) for the oriented curve specified.

\(\mathbf{F}(x, y, z)=\left\langle\frac{1}{y^{3}+1}, \frac{1}{z+1}, 1ightangle, \quad \mathbf{r}(t)=\left\langle t^{3}, 2, t^{2}ightangle\) for \(0 \leq t \leq 1\)