Hi John,
Expanding on Neil's answer:
For equally spaced points
delta = Pi/50;
data = Table[N@Sin[x], {x, 0, Pi, delta}];
Total[delta*data]
(* 1.99934 *)
For unequally spaced points you can use Interpolation
xVals = Table[x + RandomReal[{-delta, delta}/2], {x, 0, Pi, delta}];
yVals = Sin[xVals];
points = Transpose[{xVals, yVals}];
iFun = Interpolation[points]
Integrate[iFun[x], {x, Min@xVals, Max@xVals}]
(* 1.9995 *)
