# A calculus problem by 승원 진

Calculus Level 5

$\large h(x) = \int_{g(x)}^{g(x+1)} f(t) \, dt$

Consider the two functions $$f(x) = \sin(\pi x)$$ and $$g(x) = x(x+1)$$. If the function $$h(x)$$ whose domain is all real numbers, and it satisfies the equation above, how many real roots of $$h(x) =0$$ exist on the interval $$[-1,1]$$?

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