If \textbf{F} = (3x^2 + 6y)\textbf{i} - 14yz\textbf{j} + 20xz^2\textbf{k}, evaluate \int_C \textbf{F} \cdot d\textbf{r} from (0, 0, 0) to (1, 1, 1) along the\following paths C:\a. x = t, y = t^2, z = t^3.\b. the straight lines from (0, 0, 0) to (1, 0, 0) to (1, 1, 0) and then to (1, 1, 1).\c. the straight line joint (0, 0, 0) and (1, 1, 1).\ [Ans: 5, \frac{23}{3}, \frac{13}{3}]