Calculus: Early Transcendentals 8th Edition

$\int_{a}^{b}I(t)~dt~~$ represents the total amount of charge that flows through the wire from time $a$ until time $b$.
We can state the Net Change Theorem as follows: The integral of a rate of change is the net change: $\int_{a}^{b}F'(x)~dx = F(b)- F(a)$ $~~I(t)~~$ is the current in the wire, which is the rate at which charge flows through the wire each second. Therefore, $~~\int_{a}^{b}I(t)~dt~~$ represents the total amount of charge that flows through the wire from time $a$ until time $b$.