I=∫010[x]e[x]ex−1dx

In the interval k,k+1,x=k   and x+1=k+1I=∫010[x]·e[x]+1-xdx=∫010dx+∫12e2-xdx+∫232·e3-xdx+∫343·e4-xdx+….+∫9109e10-xdx                                      =-{(1-e)+2(1-e)+3(1-e)+……+9(1-e)}                                       =45e-1