If the integral \(\int_0^{10} \frac{[\sin 2 \pi x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta e^{-\frac{1}{2}}+\gamma\) where \…

If the integral \(\int_0^{10} \frac{[\sin 2 \pi x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta e^{-\frac{1}{2}}+\gamma\) where \(\alpha\), \(\beta, \gamma\) are integers and \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of \(\alpha+\beta+\gamma\) is equal to:

[JEE Main 2021, 17 Mar (Shift 2)]