I'm looking for an analytical approximation of $\int_a^b e^{-x^2}\text{erf}(x+c) dx$ that would be accurate to precision $\epsilon$ for $a,b,c$ within a certain range. How do I ask Mathematica for that?

I tried to Integrate the above expression, but no analytical solutions found.

I'm looking for an analytical approximation of $\int_a^b e^{-x^2}\mathrm{erf}(x+c) dx$ that would be accurate to precision $\varepsilon$ for $a,b,c$ within a certain range. How do I ask Mathematica for that?

I tried to Integrate the above expression, but no analytical solutions were found.