[Foreword] [The problem of areas] [Step functions] [The integral of step functions] [Properties of the integral of step functions] [A little break] [The Riemann Integral] [Other definitions of the Riemann integral] [What functions are Riemann integrable?] [Some properties of the Riemann integral] [The mean value theorem] [The integral function] [The fundamental theorem of integral calculus] [Antiderivatives and Riemann integral: some observations] [Final exercises] [The end]