Find the current i_{C} across a capacitor of 1 \mathrm{~F} as a function of time, if the voltage is given as
v_{C}(t)=\left\{\begin{aligned}t^{2}+1,\quad & 0 \leq t \leq 2 \mathrm{~s} \\t+3,\quad & 2 \leq t \leq 5 \mathrm{~s} \\-t^{2}+12 t-27,\quad & 5 \leq t \leq 6 \mathrm{~s} \\9,\quad & t \geq 6 \mathrm{~s}\end{aligned} \quad(\mathrm{~V}).\right.