Modify HTML content saved in a DB table

I have a table in a DB with a general text field which contains HTML formatted text. I need to parse the content of such a field, find all the "img" tags and perform 2 operations (only for "img" tags):

1) Remove completely the "style" attribute (if there is one).
2) Add a class="img-responsive" attribute.

For example, a simple string to be parse can be as follows:

<div>
<p>This is some text</p>
<img src="http://www.mywebsite.com/myImage.jpg" alt = "" style="width:600px; height: 400px;"/>
</div>

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Or, something more complex:

<p style="margin: 0px 0px 10px; background: white; font-size: 14.6667px; font-family: Calibri, sans-serif;"><span style="font-size: 14pt; font-family: Georgia, serif; color: #404040;">
<img src="http://www.mywebsite.com/myImage.jpg" alt="" style="width:600px; height: 898px;" />
<br /></span></p>  

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In both cases, the "img" tag should result in:

<img src="http://www.mywebsite.com/myImage.jpg" alt="" class="img-responsive" />

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I know that one option is to use regular expressions but I do not have any experience with them. I will be using C# to perform this task.
I will very much appreciate your help.

Respectfully,
Jorge Maldonado