Q:

Area under a curve in Mathematica

Problem:
I have a two separated list of values, X={x1,x2....x2059} and Y={Y1,Y2....Y2059}. Using the Mathematica function "Transpose" i can obtain a new list Z = {{x1,y1},{x2,y2},...{x2059,y2059}}. Using ListLinePlot[Z] i made the plot. 
Now, the problem is: How i can calculate the area under the plotted curve. I can't use NIntegrate, or Integrate. Can I use the interpolation function? how? 
Even using the Trapezoidal Rule (implemente by me) i didn't obtain a good resul.
The data comes from an Load-deformation plot. This means that for the first half part of the data, the curve growth. From the second part of data the curve come back to zero (close to zero). In particular, X = deformation and Y=Load.

A:

(*create a simulation for your points*)
npts = 2058;
x = Sort@RandomReal[100, npts];
y = Join[Sort@RandomReal[100, npts/2], Reverse@Sort@RandomReal[100, npts/2]];
f = Interpolation[Transpose@{x, y}, InterpolationOrder -> 1];

(*Plot and Integrate*)
Plot[f[t], {t, Min@x, Max@x}, Filling -> Axis]
NIntegrate[f[t], {t, Min@x, Max@x}, Method -> "LocalAdaptive"]

answer:
(* 5006.01 *)

