@Zhonghui
of course. you are absolutely right (and it must be the same!).
Look at
j1 = Integrate[E^(-(1 - s^2)/(2 \[Epsilon])), {s, 0, -1 + \[Epsilon] x1}]
and after the replacement
-(1 - s^2)/(2 \[Epsilon]) /. s -> -1 + x1 \[Epsilon] + u // Expand // FullSimplify
j2= Integrate[Exp[((-2 + u + x1 \[Epsilon]) (u + x1 \[Epsilon]))/(
2 \[Epsilon])] D[-1 + x1 \[Epsilon] + u, u], {u, 1 - x1 \[Epsilon],
0}]
