Question: Eliminating a discontinuity in an integrand?

I would like to calculate a definite integral in the attached file. Doing so numerically is straightforward. However, a symbolic approach initially fails due to three points of discontinuity in the integrand. Yet, these points can be remedied by taking limits. How can the domain in Maple be extended using these limits to achieve continuity across the entire domain?

testint.mw

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