  We present two lines of investigation involving anomalies. First, we review
mechanisms behind the classical and quantum conservation of symmetries using
functional integration. This discussion clarifies conditions for quantum
violations, as acknowledged in chiral theories. Then, we elucidate the subject
of gauge anomaly cancellation when all fields are quantized. Such an outcome
requires gauge invariance of the bosonic measure, so our first object is
proving this invariance within Fujikawa's approach. Second, we investigate
anomalies in fermionic perturbative amplitudes using Implicit Regularization.
The discussion of the single-axial triangle fundaments this analysis, bringing
the elements necessary to approach the single-axial box. When organizing their
mathematical structure, we highlight the role of traces involving the chiral
matrix. Choosing a specific expression for them reflects on the position of
symmetry violations, which has implications regarding the linearity of
integration. Power counting and tensor structure imply the presence of surface
terms related to momenta ambiguities. We present the results without computing
these surface terms. In this neutral perspective, we explore possibilities
achieved under different prescriptions.
