The paper presents the results of a case study examining students' difficulties in the learning of integral calculus. It sought to address the misconceptions and errors that were encountered in the students' work solution. In quantitative study, the marks obtained by 147 students of Diploma in Computer Science in advanced calculus examinations were used as a measurement to evaluate the percentages of errors. Further, qualitative study examined the types of errors performed by 70 diploma students of the advanced calculus courses in their on-going assessments. The students encountered more difficulties in solving questions related to improper integrals for standard functions (63.1 percentages of errors). The three techniques of integration, namely by parts, trigonometric substitution and partial fraction with combined percentage errors of 42.8 also contributed to this. The types of conceptual errors discovered are symbolic, standard functions recognition, property of integral and technique determination. The procedural errors are due to the confusion between differentiation and integration process while the technical errors have foreseen the students struggling with poor mathematical skills and carelessness. The results will thus be useful to Mathematics educators who are keen in designing functional teaching and learning instruments to rectify the difficulties and misconceptions problems experienced by calculus students.