Exploring New General Integral Lower Bounds Depending on Four Functions

This article focuses on the determination of appropriate lower bounds for a general term defined as the sum of two specific integrals. This term has the property of depending on four functions, one of which is associated with the two integrals involved. Two theorems are established: one with monotonicity and sign assumptions on the functions considered, and another, more technical, with special primitive-like inequality assumptions on these functions. The connections, advantages and limitations of these assumptions are discussed in detail.