Confusion with the term 'Area bounded by the curves' So I have a question:

Let $f(x) = \sqrt{\tan x}$ . Show that area bounded by $y = f(x)$, $y = f(c)$, $x = 0$ and $x = a$,  $0<c<a<\frac{\pi}{2}$ is minimum when $c=\frac{a}{2}$.

I have a problem in identifying the region of area bounded.
I thought and solved using this region:



But the solution has considered the following region:



Note:
For simplicity sake, I have considered $c=\frac{\pi}{6}$ and $a=\frac{\pi}{3}$ in this graph.
I am confused regarding the term area bounded by the curves. How do I find this region. often times I consider the wrong regions. Any help will be appreciated.

Note that your proposed region has part of its boundary determined by $y=0$ (the $x$-axis), near the bottom left. This observation shows that the region you drew isn't the intended one; all pieces of boundary of the region should be parts of one of the given equations.
(Since this is about communication and not strictly about math, it's perhaps worth adding that the onus is on the writer to make sure they don't put us in a situation where the description has extraneous information or is otherwise ambiguous; and then we trust that the writer wrote the best possible description and interpret it accordingly. A writer can also write "to the left/right of" or "above/below" to help clarify instead of just "bounded by".)
