The current in a conductor is expressed as $I = 3t ^ { 2 } + 4t ^ { 3 }$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t = 1 \mathrm {~s}$ to $t = 2 \mathrm {~s}$ is $\_\_\_\_$ C.