I noticed that MathJax is incorrectly rendered.
Here https://www.emathhelp.net/calculators/calculus-2/integral-calculator/?f=xsinx&var=&steps=on
under "the integral of the cosine is ..." only integral of cosine on left-hand-side and sine on the right-hand side should be red, not equal sign and -xcos(x).
However, when I click "show math as tex commands", I get - x \cos{\left(x \right)} + \color{red}{\int{\cos{\left(x \right)} d x}} = - x \cos{\left(x \right)} + \color{red}{\sin{\left(x \right)}} and this is the string without any errors.
What is causing incorrect color rendering?
The site you link to uses the color extension for MathJax, which redefines the \color macro to be compatible with the LaTeX version. In LaTeX, \color is a switch that changes the color from there on, rather than MathJax's version where \color takes an argument that is what to be colored. So something like \color{red}{x} + y usually would produce a red "x" and a black "+ y", but with the color extension would produce red "x + y". This is why you are seeing completely red expressions in the website you linked to.