calculus and analysis – Evaluating a 2d integral

I would like to calculate this integral

begin{align*}
I(s_1,s_2,s_{12},m) =
int_{0}^{1} {rm d}x int_{0}^{1-x}
{rm d}y Big(
x y
Big(
y(1-y)s_1 + x(1-x)s_2 + 2 xy s_{12} -m^2
Big)^{-1}
Big),
end{align*}

where $s_{1}, s_{2}, s_{12}$ and $m$ are constant real values.

To evaluate this integral, I’ve used

$Assumptions = Element({s1, s2, s12, m}, Reals) &&  s1 >= 0 && s2 >= 0 && m > 0; 

FullSimplify(
  Integrate(Integrate(
    x*y/(y*(1 - y)*s1 + x*(1 - x)*s2 + 2*x*y* s12 - m^2), {y, 0, 1 - x}), {x, 0, 1})) // Timing

This evaluation is very slow, and I wasn’t able to get the final result. Does anyone have a suggestion to speed up the calculation?