It's quite common that students will confuse \(\sin(x^2)\) with \(\sin^2(x)\). If this were the case, then they would be equal, and thus \(\sin^2(x)-\sin(x^2)\) would equal \(0\). This isn't the case however. Define this function as \(f(x)\). Find

\(\displaystyle\int_{0}^{100} f(x)\) \(dx\).

Round to the nearest whole number.

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