This paper answers three research questions: (1) What mathematical connections do preuniversity students make when they solve tasks (algebraic, graphical and application problems) of Calculus that involve the derivative and the integral?, (2) What is the relationship between those mathematical connections that pre-university students make and how they contribute to mathematical understanding of the Fundamental Theorem of Calculus?, and (3) What alternative conceptions appear when pre-university students solve tasks (algebraic, graphical and application problems) of Calculus that involve the derivative and the integral?