How to kern kpfont integrals?

Question

kpfont integrals have a lot of empty space both on the left and on the right ever with smashoperator:

How do I kern the function "into" the integral and reduce the white space of the left document-wide?

\documentclass{article}

\usepackage[intlimits]{kpfonts}
\usepackage{amsmath,mathtools}

\begin{document}
\begin{equation}
I = \int_{t_{k}}^{t_{k+1}} f(t) dt
\end{equation}

\begin{equation}
SMOP = \smashoperator{\int_{t_{k}}^{t_{k+1}}} f(t) dt
\end{equation}
\end{document}

Answer 1

I have found a partial solution in How can I redefine \int to put a negative space after the integral sign, but keep the limits properly set?

\usepackage{xparse}
\RenewDocumentCommand{\int}{e{_^}}{%
  \DOTSI
  \intop_{\IfValueT{#1}{#1}}^{\IfValueT{#2}{#2}}%
  \mspace{-4mu}%
}