Holomorphism check for the functions $F(z)=\int_{-\infty}^\infty e^{(t-z)^2}dt$ and $G(z)=\int_{-\infty}^\infty e^{|t-z|^2}dt$

Question

Which one is holomorphic and why, out of: $$F(z)=\int_{-\infty}^\infty e^{(t-z)^2}dt$$ and $$G(z)=\int_{-\infty}^\infty e^{|t-z|^2}dt$$ I tried using residues (calculating the integral and checking the holomorphism property), but have not succeeded. Need another way.Perhaps without calculating the integrals.