Hint Resolve (integral0 RtoK) (integral1 RtoK) (@monicXsubC K) : core.
Let XsubC0 (u : K) : root ('X - u%:P) u. Proof. by rewrite root_XsubC. Qed.
Let intR_XsubC u :
integralOver RtoK (- u) -> {in 'X - u%:P : seq K, integralRange RtoK}.

(* Specifications: *)
Lemma integral_add u v :
integralOver RtoK u -> integralOver RtoK v -> integralOver RtoK (u + v).