When you look at the facade of the Cathedral of Notre Dame in Paris, what do you see? The rectangular towers, classical Gothic arches, massive domes and stained glass rose windows of this famous cathedral offer excellent examples of areas for students to calculate via integration. Most modern calculus texts use simple examples of finding the area of an ellipse or circle when incorporating trigonometric substitution. This article describes an approach for instructors of single variable integral calculus courses in calculating the areas and volumes of Gothic structures which have incorporated the quinto acuto arch. Further, students do not have to travel far to find examples of Gothic architecture near their own campuses. Examples and sample calculations are provided.