Based on the output of the function activeSetLogCon, this 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
$$I_j(x) = \int_{x_j}^x \widehat{F}(r) d r =
(x-x_j)\widehat{F}(x_j)+\Delta x_{j+1}\Bigl(\frac{\Delta x_{j+1}}{\Delta
\widehat\varphi_{j+1}}J\Bigl(\widehat\varphi_j,\widehat\varphi_{j+1},
\frac{x-x_j}{\Delta x_{j+1}}\Bigr)-\frac{\widehat f(x_j)(x-x_j)}{\Delta
\widehat \varphi_{j+1}}\Bigr)$$
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.
Note that this version of intF is similar to that in the logcondens package, versions
1.3.5 and earlier. Newer versions of that package have modified
arguments. Here, we have also added the argument 'prec'.