If, for all real number x, f(x) = g(x) + 5, then on any interval [a, b], what is the area of the region between the graphs of f and g?

Answer 1

∫f(x)dx over [a,b] = ∫(g(x)+5)dx over [a,b].

By Addition rule of integrals, ∫(g(x)+5)dx = ∫g(x)dx + ∫5dx.
= ∫g(x)dx + 5(b-a)