Given $$F(t_1,t_2,\dots,t_n)=\int\frac{P_1(x_1,x_2,\dots,x_n)}{P_2(x_1,x_2,\dots,x_n)}dx_1dx_2\dots dx_n$$ where $P_1(x_1,x_2,\dots,x_n), P_2(x_1,x_2,\dots,x_n)$ are polynomials whose coefficients are over $\mathbb{Q}$ or $\mathbb{\bar{Q}}$ , $\Delta$ are domain given by polynomial inequalities with coefficients over $\mathbb{Q}$ or $\mathbb{\bar{Q}}$.
Now is the function $F(t_1,t_2,\dots,t_n)$ where $(t_1,t_2,\dots,t_n)\in \Delta$,a semi-algebraic function?