Kindly verify this integral calculation

I don't consider myself a super expert in calculus but I ain't bad either. Here, I am unable to comprehend the following two calculations (comments and indication marked in the images), please clarify where I am wrong:

and this is also from the same page (https://brilliant.org/wiki/conservative-forces/)

#Mechanics

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

@Techy samco in first image you are correct.

Talulah Riley - 10 months, 2 weeks ago

@Aruna Yumlembam

Yajat Shamji - 10 months, 2 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$