This notation is not used in any English-speaking country that I know of. It appears to be peculiar to France; your source, Euronews, is headquartered in France. Almost anywhere else this will be represented with a . or : replacing the h, or with no separator—so-called ‘military time’.
As Happy tells you, 24-hour notations are read among the military as “so-many-hundred hours”. In civilian speech, however—in the US, at least, and I think this is probably true elsewhere in the English-speaking world—24-hour notation is often, perhaps usually, “translated” into 12-hour terms, so 15h00 would be spoken as “three pee-em”, representing 3:00 pm.
But as Jolenealaska points out, many civilians in the US are familiar with the ‘military’ reading, and that familiarity is growing with the spread of the internet, where timestamps are commonly expressed in 24-hour notation. The main thing is to employ the form your hearers will be comfortable with. Use the military version with people you expect to understand it, use the translated reading if you’re not sure.
It would normally be read aloud as:
f of x equals x squared
There are some variations you might hear. For example, sometimes is is used in place of equals.
If the exponent was 3, you would say cubed. Anything higher than three (say, for example, 5) would generally be read aloud as:
f of x is x to the fifth (power)
or perhaps:
f of x is x to the power of five
Best Answer
If it is clear that i and n are one-indexed, then "the sum from i equals one through i equals n" can be replaced by "the sum of the first n terms". "The width of each i" is an interpretation of "delta i".
"Goes to" can be replaced by "goes toward", or (as Damkeng suggests) "tends to", or (as J.R. suggests) "approaches".
I often use a notation like "integral from x equals a to x equals b" instead of "integral from a to b". I also often say "to positive infinity" instead of "to infinity".
I "factored out" the definition of the function in the first sentence. If the function were easy to say (such as "x squared"), I would not "factor out" the definition of the function. Instead, I would include the "x squared" in the statements of the integrals, a la Damkeng's answer.