Is there a vertical bar as long as the integral sign?

Question

I'm looking for a big vertical bar that puts the lower and upper elements at the same height as on the default integral sign. Currently, using \Big| (or \Bigr|), and \bigg| (or \biggr|) gives an ugly output. Here's a MWE to show my issue:

\documentclass[11pt,letterpaper,twoside]{book}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[total={6in,10in},left=1.5in,top=0.5in,includehead,includefoot]{geometry}
\usepackage{microtype}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{mathtools}
\usepackage{tensor}

\begin{document}

\begin{gather*}
    \int_{-\, a}^{+\, a} f(x) \frac{d}{dx} \: \Theta(x - \tensor{x}{_0}) \, dx \\[2ex]
\begin{aligned}
    &= f(x) \, \Theta(x - \tensor{x}{_0}) \biggr|_{-\, a}^{+\, a} - \int_{\tensor{x}{_0}}^a \frac{d}{dx} \: f(x) \, dx \\[2ex]
    &= f(x) \, \Theta(x - \tensor{x}{_0}) \Bigr|_{-\, a}^{+\, a} - \int_{\tensor{x}{_0}}^a \frac{d}{dx} \: f(x) \, dx \\[2ex]
    &= f(a) - f(x) \biggr|_{\tensor{x}{_0}}^a = f(a) - f(x) \Big|_{\tensor{x}{_0}}^a.
\end{aligned}
\end{gather*}

\end{document}

Preview of what this code is doing:

So what am I doing wrong with this code? How could I draw a vertical bar that puts its two elements exactly at the same position as an integral sign?

(note that I'm using the tensor package for another reason, not relevant here)

---

EDIT:. I could define a custom vertical bar of the same size as the integral sign using the scalerel package:

\usepackage{scalerel}
\newcommand*{\eval}{\stretchrel*{|}{\int}}

but then the lower and upper elements aren't placed at the proper position. So no luck here.

Answer 1

Define \def\myvert{\biggr|{\vphantom{\int}}} and use \myvert_{..}^{..} instead \biggr|_{..}^{..}.

Edit: If you want to have equal size of the bar and the \int then you can define it as \vrule:

\def\myvert{{\mkern2mu\vrule\,\vphantom{\int}}}

Answer 2

Combining wipet's answer and a scaled up version of |, I get good results:

\documentclass[11pt,letterpaper,twoside]{book}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[total={6in,10in},left=1.5in,top=0.5in,includehead,includefoot]{geometry}
\usepackage{microtype}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{mathtools}
\usepackage{tensor}
\usepackage{scalerel}
\newcommand*{\eval}{\stretchrel*{|}{\int}{\vphantom{\int}}}

\begin{document}

\begin{gather*}
    \int_{-\, a}^{+\, a} f(x) \frac{d}{dx} \: \Theta(x - \tensor{x}{_0}) \, dx \\[2ex]
\begin{aligned}
    &= f(x) \, \Theta(x - \tensor{x}{_0}) \biggr|_{-\, a}^{+\, a} - \int_{\tensor{x}{_0}}^a \frac{d}{dx} \: f(x) \, dx \\[2ex]
    &= f(x) \, \Theta(x - \tensor{x}{_0}) \eval_{-\, a}^{+\, a} - \int_{\tensor{x}{_0}}^a \frac{d}{dx} \: f(x) \, dx \\[2ex]
    &= f(a) - f(x) \eval_{\tensor{x}{_0}}^a = f(a) - f(x) \Big|_{\tensor{x}{_0}}^a.
\end{aligned}
\end{gather*}

\end{document}

Preview:

I'm wondering if there's a simpler or better way of getting the same result.