Who really invented the integration symbol?

Most of the sources online say that Leibniz invented the sign. There's also this answer on this site which says so.

That is fine. But recently when I was watching Cosmos, I noticed this:

See the integration sign on the wall? That's Newton's house. Was it a co-incidence that Leibniz used the same symbol for integration?

• You mean... it's not due to Stradivarius? !strad – Gerald Edgar Feb 5 '15 at 22:32
• Integration symbol was not "discovered". It was invented. It did not exist before it was invented. Integral existed but the symbol did not:-) – Alexandre Eremenko Feb 5 '15 at 22:39
• @Alexandre Eremenko I would say integrals were discovered because math is ahuman invention. – Yashbhatt Feb 6 '15 at 1:30
• @Yashbhatt: I strongly disagree, and most mathematicians share my opinion. – Alexandre Eremenko Feb 6 '15 at 3:40

The sign of the integral was proposed by Leibniz (for indefinite integral). It is a stylized letter $S$, and $S$ stands for the "sum".
Remark. The modern notation for definite integral $$\int_a^b$$ was invented by J. Fourier.