Hmm... If he wants to find the area of a union between two graphs, what you say is not entirely applicable. The area under the union is NOT the areas of each of the graphs summed, because there are overlapping portions that will be added twice.

What you said is true, if g is one function and f is another, then I(f+g) = I(f) + I(g) but he needs a union - not a sum. And for linear functions, F(union of A and B) = F(A) + F(B) - F(intersection of A and B)