To evaluate the definite integral , we proceed step-by-step: 1. Find the Antiderivative of : The antiderivative of is obtained by applying the power rule of integration. The power rule states that for any function of the form (where ): For , the power rule gives: This means the antiderivative of is . 2. Evaluate the Definite Integral: To evaluate the definite integral, we use the Fundamental Theorem of Calculus. According to this theorem, if is the antiderivative of , then: Here, the limits of integration are 0 and 1. Thus, we need to evaluate: Now, we substitute the upper and lower limits of integration: - When , , - When , . Subtracting these values: Thus, the value of the integral is .