Answer
$\displaystyle \int f(x)dx$ represents the total cost of manufacturing $x$ items.
Units for $\displaystyle \int f(x)dx$ = $\text{(units of f)}\times\text{(units of x)}$
Work Step by Step
See section 11-2, Marginal Analysis$:$
The marginal cost function $C'(x) $is the derivative of the cost function $C(x)$.
So, $C(x)$ is an antiderivative of $C'(x)$.
The unit of $x$ is "items produced".
If $f(x) $represents dollars per item, it has the same units as marginal cost, $C'(x)$.
The units of $\displaystyle \int f(x)dx$ are the same as units of $C(x)$, dollars.
$C'(x)$ has units $\displaystyle \frac{\text{units of C}}{\text{units of x}}$
We can obtain the unit for $C(x)=$ unit for $\displaystyle \int f(x)dx$
$= \text{(units of C')}\times\text{(units of x)}$
$= \text{(units of f)}\times\text{(units of x)}$
