In Colleges of Technology, which conducts engineering education, mathematics is necessary for the students to learn engineering major subjects. It has been claimed that the students can properly use mathematics in theoretical part of the major subjects. They are required not only for calculation abilities but also for understanding mathematical concepts in engineering. I would like to point out two requirements for the students properly to use mathematics in the major subjects as follows; (i) Students need to consider mathematics in the major subjects shares the same content with that in regular mathematics class. (ii) Students need to image the mathematical concepts. Based on theses requirements for the students, I would like to propose what we can actually do in regular mathematics class for the first and second year students from the perspective of initial engineering education at National Colleges of Technology as follows. (i) I would like to propose teaching materials that students can readily conceptualize what integral is in two credit hours before studying integral. (ii) I would like to propose visual teaching materials that students can readily verify results of indefinite integral from graphs and figures.