We study the existence of positive solutions to the three-point integral boundary value problem u′′+a(t)f(u)=0, t∈(0,1), u(0)=0, α∫0ηu(s)ds=u(1), where 0<η<1 and 0<α<2/η2. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.