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Let's break down and solve both of these problems step by step. ### Problem 1: Evaluate the integral We are tasked with evaluating the integral: \[ \int_{0}^{1} x^{2} \, dx \] To solve this using Riemann integration, we'll compute it using the fundamental theorem of calculus. First, find the indefinite integral of \( x^2 \): \[ \int x^2 \, dx = ___ ________ _________ ________ ____ ________ ______ ______ ______ __________ ______ _______.
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