  Using the Laplace derivative a Perron type integral, the Laplace integral, is
defined. Moreover, it is shown that this integral includes Perron integral and
to show that the inclusion is proper, an example of a function is constructed,
which is Laplace integrable but not Perron integrable. Properties of integrals
such as fundamental theorem of calculus, Hake's theorem, integration by parts,
convergence theorems, mean value theorems, the integral remainder form of
Taylor's theorem with an estimation of the remainder, are established. It turns
out that concerning the Alexiewicz's norm, the space of all Laplace integrable
functions is incomplete and contains the set of all polynomials densely.
Applications are shown to Poisson integral, a system of generalised ordinary
differential equations and higher-order generalised ordinary differential
equation.
