Generalize the use of size_t in TimeIntegration

Issue/feature addressed

int, size_t, and unsigned int are used inconsistently in the TimeIntegration module.

Proposed solution

Generalize the use of size_t in TimeIntegration

Tests

Suggested reviewers

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Notes

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Checklist

• [ ] Functions and classes, or changes to them, are documented.
• [ ] User guide/documentation is updated.
• Changelog is updated.
• [ ] Suitable tests added for new functionality.
• Contributed code is correctly formatted. (See the contributing guidelines).
• [ ] License added to any new files.
• No extraneous files have been added (e.g. compiler output or test data files).