Wolfram Alpha can't numerically integrate functions given in a table?

Question

Mathematics

This doesn't work:
Simpson's Rule {{1,0},{2,2},{3,7},{4,11},{5,12},{6,6},{7,2}} on [2,3] with interval size 0.2
and
Simpson's Rule {{x1,y0},{x2,y2},{x3,y7},{x4,y11},{x5,y12},{x6,y6},{ x7,y2}} on [2,3] with interval size 0.2
and
integrate {{1,2},{2,4},{3,8},{4,9},{5,7},{6 ,6},{7,4}} trapezoidal rule on [1,7] with interval size 0.2
And this works:
linear fit {1,2},{2,4},{3,3
} I seem to be using the same one.
How can you calculate the given functions in a table in such systems?

Answer 1

Well, that's right: it integrates functions, not a set of points. In the last example, you used regression to get a function from the points and he integrated it.