Step 1: Identify the integral you need to solve: ∫_0^1 (x^2 + 1) dx.
Step 2: Break down the integral into two parts: ∫_0^1 x^2 dx + ∫_0^1 1 dx.
Step 3: Calculate ∫_0^1 x^2 dx. The antiderivative of x^2 is (x^3)/3.
Step 4: Evaluate (x^3)/3 from 0 to 1: (1^3)/3 - (0^3)/3 = 1/3 - 0 = 1/3.
Step 5: Calculate ∫_0^1 1 dx. The antiderivative of 1 is x.
Step 6: Evaluate x from 0 to 1: 1 - 0 = 1.
Step 7: Add the results from Step 4 and Step 6: (1/3) + 1 = (1/3) + (3/3) = 4/3.
Step 8: The final answer is 4/3.
Definite Integral – The question tests the ability to evaluate a definite integral, which involves finding the area under the curve of the function between specified limits.
Integration of Polynomials – The question requires knowledge of how to integrate polynomial functions, specifically the power rule for integration.
