This paper is concerned with the second-order singular Sturm–Liouville integral boundary value problems - u ″ ( t ) = λ h ( t ) f ( t , u ( t ) ) , 0 < t < 1 , α u ( 0 ) - β u ′ ( 0 ) = ∫ 0 1 a ( s ) u ( s ) ds , γ u ( 1 ) + δ u ′ ( 1 ) = ∫ 0 1 b ( s ) u ( s ) ds , where λ > 0 , h is allowed to be singular at t = 0 , 1 and f ( t , x ) may be singular at x = 0 . By using the fixed point theory in cones, an explicit interval for λ is derived such that for any λ in this interval, the existence of at least one positive solution to the boundary value problem is guaranteed. Our results extend and improve many known results including singular and non-singular cases.