Based on an object of class dlc as output by the function logConDens,
this function gives values of
$$\widehat I(t) = \int_{x_1}^t \widehat{F}(r) d r$$
at all numbers in \(\bold{s}\). Note that \(t\) (so all elements in \(\bold{s}\)) must lie in
\([x_1,x_m]\). The exact formula for \(\widehat I(t)\) is
$$\widehat I(t) = \Bigl(\sum_{i=1}^{i_0} \widehat{I}_i(x_{i+1})\Bigr)+\widehat{I}_{i_0}(t)$$
where \(i_0 = \)min\(\{m-1 \, , \ \{i \ : \ x_i \le t \}\}\) and
$$I_j(x) = \int_{x_j}^x \widehat{F}(r) d r = (x-x_j)\widehat{F}(x_j)+\Delta x_{j+1}\Bigl(\frac{\Delta x_{j+1}}{\Delta \widehat\phi_{j+1}}J\Bigl(\widehat\phi_j,\widehat\phi_{j+1}, \frac{x-x_j}{\Delta x_{j+1}}\Bigr)-\frac{\widehat f(x_j)(x-x_j)}{\Delta \widehat \phi_{j+1}}\Bigr)$$
for \(x \in [x_j, x_{j+1}], \ j = 1,\ldots, m-1\), \(\Delta v_{i+1} = v_{i+1} - v_i\) for any vector \(\bold{v}\)
and the function \(J\) introduced in Jfunctions.