Kata

Let $f(n)={\int }_0^n\lfloor x\rfloor x\lceil x\rceil dxf(n)\; =\; \backslash int\_0^n\backslash ,\backslash lfloor\; x\backslash rfloor\backslash :x\backslash :\backslash lceil\; x\backslash rceil\backslash ;\; dx$

where $\lfloor x\rfloor \backslash lfloor\; x\backslash rfloor$ denotes the greatest integer smaller than or equal to x (floor function),
and $\lceil x\rceil \backslash lceil\; x\backslash rceil$ denotes the smallest integer greater than or equal to x. (ceiling function)

Examples:

⌊6.7⌋ = 6
⌈4.3⌉ = 5

Task

Given a positive integer n, return the value of f(n) mod 1000000007.

1 <= n <= 10^5

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Credit: I saw this interesting question on a Prime Newtons video.

His channel is here: https://www.youtube.com/@PrimeNewtons

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Also, please check out the rest of the katas in this series! https://www.codewars.com/collections/math-challenges-1

appreciate any feedback given, thank you!