Integral Calculus: JEE Main 2021 Mathematics question

If the integral $\int_0^{10} {{{[\sin 2\pi x]} \over {{e^{x - [x]}}}}} dx = \alpha {e^{ - 1}} + \beta {e^{ - {1 \over 2}}} + \gamma$, 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 :