What do you exactly mean by the area bounded when it comes to integration

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I am trying to understand this term when it comes to integrating the function to find out areas.

Is it correct to say that for the curve $y=e^{(x-1)/2}-2$, is the shaded region is bounded by the following?

  • the curve
  • $x$-axis
  • $y$-xis
  • the line $x=3$

example

If we consider the next shaded area for the curve $y=x(x-1)$, is it correct to say that the shaded area is bounded by:

  • the curve
  • the $x$-axis
  • the line $x=1$
  • and the line $x=0$ (this one I am not sure)

example2

Can someone please clarify this for me?

Thank you.