Explanation

∫01​(2x+1)dx

Step 1: Integrate the function

We integrate each term separately:

$$int (2x + 1), dx = int 2x, dx + int 1, dx = x^2 + x + C$$

Step 2: Apply the limits from 0 to 1

$$left[ x^2 + x right]_0^1 = (1^2 + 1) - (0^2 + 0) = 1 + 1 = 2$$