All 4 Uses of

integrity
in
The Scarlet Letter

…of integrity, that, like most of his other endowments, lay in a somewhat heavy mass, and was just as unmalleable or unmanageable as a ton of iron ore;
p. 22.5

integrity = strong moral principles

His integrity was perfect; it was a law of nature with him, rather than a choice or a principle;
p. 25.0 *

integrity = quality of strong moral principles

He had begun an investigation, as he imagined, with the severe and equal integrity of a judge, desirous only of truth, even as if the question involved no more than the air-drawn lines and figures of a geometrical problem, instead of human passions, and wrongs inflicted on himself.
p. 119.2

integrity = moral principles

In that old day the English settler on these rude shores—having left king, nobles, and all degrees of awful rank behind, while still the faculty and necessity of reverence was strong in him—bestowed it on the white hair and venerable brow of age—on long-tried integrity—on solid wisdom and sad-coloured experience—on endowments of that grave and weighty order which gave the idea of permanence, and comes under the general definition of respectability.
p. 221.8

Definitions:

(1) (integrity as in: a person of high integrity)
having strong moral principles -- especially honesty
(2) (integrity as in: system integrity)
having a proper, unbroken state