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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