## Calculus, 10th Edition (Anton)

Assuming that $f$ and $g$ differ by a constant $c$ signifies that $g$=$f+c$. Therefore, the area formula becomes $\int{f(x)+c-f(x)}dx$ on the interval $[a,b]$, or $\int{c}dx$ on $[a,b]$. Integrating and using the Fundamental Theorem of Calculus yields $c(b-a)$.