Calculating charge when current is a piecewise function
You goofed the integration.

\$ \int_0^1 4dt + \int_1^2 4t^2dt \\
= \rvert_0^1 4t + \rvert_1^2{4\over3}t^3\\
= 4(1) - 4(0) + {4\over3}(2)^3 - {4\over3}(1)^3\\
= 4 + {28\over3}\\
= {40\over3}\$