Answer
Net charge is 2 C.
Work Step by Step
To find charge we must integrate the current over time. $$q(t) = \int_{t_{0}}^{t}i(t) dt + q(t_{0})$$
So: $$q(\infty) = \int_{0}^{\infty}2e^{−t} dt$$ $$q(\infty)=-2e^{-\infty}-(-2e^0)$$$$q(\infty)=0+2$$
