Find the antiderivative function f (x) = 2x + 3, the graph of which passes through the point M (1; 2).

To find the antiderivative F (x) of the function f (x) = 2x + 3, find the indefinite integral using the properties and the table of integrals:

F (x) = ∫ (2x + 3) dx = ∫2xdx + ∫3dx = x ^ 2 + 3x + C.

To find the antiderivative that passes through the point M (1; 2), we substitute the coordinates of the point M into the found integral F (x) = x ^ 2 + 3x + C: 2 = 1 ^ 2 + 3 * 1 + C → C = 2 – 4 = -2.

Hence, the antiderivative that passes through the point M (1; 2) has the form: F (x) = x ^ 2 + 3x – 4.