Consider a vector field \(\vec{F} = (x^2 - y^2) \hat{i} + 2xy \hat{j}\) in two-dimensional space. Evaluate the line integral of \( \vec{F}\) along the curve C parameterized as \( \vec{r}(t) = t \hat{i} + t^2 \hat{j}\) for t in [0, 1].