Integrate $f(x, y, z) = x + \sqrt{y} - z^2$ over the path from $(0, 0, 0)$ to $(1, 1, 1)$ (see accompanying figure) given by
$C_1: \mathbf{r}(t) = t\mathbf{i} + t^2\mathbf{j}$, $0 \le t \le 1$
$C_2: \mathbf{r}(t) = \mathbf{i} + \mathbf{j} + t\mathbf{k}$, $0 \le t \le 1$