Introductory university physics frequently requires students to construct integrals. To explore students' abilities with this skill, we administered a simple physics problem requiring the construction of an integral to students enrolled in calculus-based introductory physics. Half of these students received written questions intended to scaffold construction of the integral, and the other half were not provided with scaffolding. Results indicate a strong interaction between scaffolding and student course grade. Specifically, students whose final class grade was above the median benefited significantly from the scaffolding, but students with grades below the median were not helped by the scaffolding. We also searched for other knowledge and skill factors that may inform instruction to improve integral construction skills, including spatial reasoning and conceptual understanding of the integral. Moderate, independent correlations with integral score were found for each, suggesting that instruction in these areas may positively influence performance.