In this paper we show that we can offer a study of integral equations of the form x(t)= a(t)- ∫0tC(t, s)[x(s)+G(s, x(s))]ds by placing conditions on either the first or the second coordinate of C. One obtains parallel theories yielding L∞ results by working with the second coordinate, or L¹ results by working with the first coordinate. Both lines of study are quite elementary.