http://www.webassign.net/waplots/1/8...cdd54a0cb9.gif find the area of the shaded region

My work: http://latex.codecogs.com/png.latex?...20-%20e^y)\,dy

http://latex.codecogs.com/png.latex?...^1_{\text{-}1}

http://latex.codecogs.com/png.latex?...xt{-}1}\right]

http://latex.codecogs.com/png.latex?...c{1}{e}\right)

http://latex.codecogs.com/png.latex?...c{1}{e}\right)

http://latex.codecogs.com/png.latex?...{1}{e}%20-%20e

. http://latex.codecogs.com/png.latex?...frac{1-e^2}{e}

this is my final answer but I am wrong. Can someone suggest where I went wrong? Thanks!