  This paper introduces the target sum function along with its characteristics.
The target sum function takes a list of integers and a specific target integer
as input values and expresses the number of ways to obtain the target sum by
either adding or subtracting all of the integers from the given list. This
function is rooted in the target sum problem which is explored in the fields of
computer science and combinatorics. This paper, following the establishment of
the generalized Werner's formula, will propose a link between the target sum
function and the definite integral of the product of sine and cosine functions
based on the formula.
