Tell MMA that $\int_0^1 \alpha \beta(x) dx= \alpha \int_0^1 \beta(x) dx$

Question

Why is it that MMA excludes alpha from the integral in the first case but not in the second?

Integrate[alpha*beta[x],x] 
(* alpha Integrate[beta[x], x] *)

Integrate[alpha*beta[x], {x, 0, 1}]
(* Integrate[alpha*beta[x], {x, 0, 1}] *)

and how to have Integrate[alpha*beta[x], {x, 0, 1}] return alpha*Integrate[beta[x], {x, 0, 1}]?