Total change via the Net Change Theorem

By the Net Change Theorem, the total change in accumulation is $\int_1^3 (4x^3 - 6x)\,dx$, since integrating the rate of change $f'(x)$ over the interval gives the net change in $f(x)$. An antiderivative of $4x^3 - 6x$ is $F(x) = x^4 - 3x^2$.

Evaluating, $F(3) = 3^4 - 3(3)^2 = 81 - 27 = 54$ and $F(1) = 1^4 - 3(1)^2 = 1 - 3 = -2$. The total change is $F(3) - F(1) = 54 - (-2) = 56$ grams.