Quick question about a picture - area under a normal distribution is always 1 Check out the picture below.
It's from this site: http://mathworld.wolfram.com/Convolution.html
All 3 curves (red, blue, green) are normal distributions [Edit and solution to my question (thanks Hyperplane): Turns out they are not the curves of a normal distribution. I learned "Gaussian" does not necessarily mean a probability density function]. Green is the convolution of blue and red.
My question
I know the area under all normal curves is one (axiom of probability). But it seems like the red curve has the biggest area.
I know the convolution of two normals has a variance equal to the sum of the variance of $f$ and $g$... I feel this is a bad picture, but I know I'm wrong to accuse wolfram of that. Can you fix my intuiton? Is it really just all in the tails?
Sorry if this is the dumbest question ever.

 A: You are right. The picture (and text) is misleading. To check that, look at the boxcar function. The area of $f$ and $g$ is definitely different
A: Why do you assume they are all probability densities?
To me it seems like they simply chose $g(x) = \tfrac{1}{2}f(2x)$. Hence green and blue should have the same area, but not blue and red.
I manged to recreate it in desmos. It appears that they used $f(x) = e^{-(2x)^2}$ and $g(x) =\frac{1}{2}e^{-(4x)^2}$, which gives $[f*g](x) = \frac{1}{4}\sqrt{\frac{\pi}{5}}e^{-\tfrac{16}{5}x^2}$. (Or values that are at least very close to this)

A: The picture is not correct as Hyperplane has shown us.
So the areas are not equal.
Note that such a "huge-area-under-a-small-function-nuance" illusion does exist for other functions. We can compare the convergent integral
$$\lim_{t\to\infty}\int_1^t\frac{1}{x^2}dx=\lim_{t\to\infty}(1-\frac{1}{t})=1$$
and the divergent integral
$$\lim_{t\to\infty}\int_1^t\frac{1}{x}dx=\lim_{t\to\infty}\ln(t)=\infty$$
Both functions $\frac{1}{x^2}$ and $\frac{1}{x}$ are very close to $0$ for $x>4$, but still the second integral keeps adding an unbounded amount of area as $t$ gets larger.
