Is it possible to tell *Mathematica* to find the lower and upper limits of the following function

```
fun(x1_, x2_, y1_, y2_) =
1/2 (2 x1 (1 - y1) + 2 x2 (1 - y2) + x1 x2 (-2 + y1 + y2));
```

where $0le x_1 le 1$, $0le x_2 le 1$, $0le y_1 le 1$, and $0le y_2 le 1$.