The area under a curve between two points can be found by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. Areas under the x-axis will come out negative and areas above the x-axis will be positive.Since we are assuming that f is continuous on [0,a], it is continuous on the interval with endpoints b and b+h (I say it this way because h could be negative). ... Then m(h)≤f(x)≤M(h) for all x in the interval, so we know, since the integral is the area. A double integral over three coordinates giving the area within some region , If a plane curve is given by , then the area between the curve and the x-axis from to is given by. SEE ALSO: Integral, Line Integral, Lusin Area Integral, Multiple Integral, Surface Integral, Volume Integral.If a function is strictly positive, the area between it and the x axis is simply the definite integral. If it is simply negative, the area is -1 times the definite integral. ... First the area between y=f of x some curve and the x axis from x=a to x=b.