Show that the ‘Linear Accumulation Function’ is valid for all real numbers.

To show that the Linear Accumulation Function is valid for all real numbers, we need to demonstrate that it satisfies the necessary conditions and properties.

The Linear Accumulation Function, denoted by A(x), is defined as the integral of a given function f(t) with respect to the variable t, evaluated from a fixed point a to x:

A(x) = ∫[a, x] f(t) dt

To establish the validity of the Linear Accumulation Function for all real numbers, we need to prove two essential properties: additivity and continuity.

1. Additivity:
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