I need to use the discrete fourier transform for function that represented as list of values. 
I started from the easy task to check am I use it right - try to reach the amplitude values fot 2*Sin[x] function. Looks like it should be somwhere about 2. But using the discrete 'Fourier' operation it is different. Can someone tell me - where is my mistakes?

Please see my observations:

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 reach fo the 'Fourier' operation the same results as I reach for the 'FourierTransform'?

Thank you for help.