Not that Snake!

Calculus Level 5

Let $$f(x)$$ be a function satisfying $$f(x)= x-x^2$$ where $$0\leq x \leq 1$$, and $$f(x+1) = f(x)$$ for $$x\in \mathbb R$$.

If $$\displaystyle g(x)= \int_0^x f(t) \, dt$$, find $$g(6.3)$$.

Notation: $$\mathbb R$$ denotes the set of real numbers.

Bonus: Find the general expression for $$g(x)$$.

See its sister problem: Not that Snake again!

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