I need to use the discrete Fourier transform for function that represented as list of values. 

I started with an easy task to check my understanding. I tried to get the amplitude values for `2*Sin[x]`. I think they should be somwhere about 2. But using the discrete `Fourier` operation produces something quite different. Can someone tell me where my mistakes are?

Here is what I tried.

    data = Table[2*Sin[x], {x, 0, 100}];
    ListPlot[data, Joined -> True]

![enter image description here][1]

    ListPlot[Abs[Fourier[data]], Joined -> True, PlotRange -> All]

![enter image description here][2]

    ListPlot[
      Table[Abs[FourierTransform[2*Sin[x], x, w]] /. 
        DiracDelta -> DiscreteDelta, {w, 0.1, 10, 0.1}], 
      Joined -> True, 
      PlotRange -> All]

![enter image description here][3]

  [1]: https://i.sstatic.net/YtAVI.jpg
  [2]: https://i.sstatic.net/ND47Q.jpg
  [3]: https://i.sstatic.net/0wyzX.jpg

How can I get the same results from 'Fourier' as I get from 'FourierTransform'?