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<p>Why does this work? When our values of <code>x</code> are less than <code>delta + 1</code> (so, when they’re near <code>delta</code>, given that our lower bound of integration is equal to <span class="math inline">\(\delta\)</span>), we pass <code>xc</code> as an argument to our <code>shift_lognormal_pdf</code> function. This way, instead of dealing with <code>x - delta</code> in <code>shift_lognormal_pdf</code>, we are working with <code>xc - delta</cod