Suppose that f is a positive continuous function defined on a finite interval [a,b) but has a vertical asymptote at b. Let S be the unbounded region under the graph of f and above the x-axis between a and b. (For Type 1 integrals, the regions extended indefinitely in a horizontal direction. Here the region is infinite in a vertical direction.) The area of the part of S between a and t is `A(t)=int_a^t f(x)dx`.