If you had numeric values for A, B, and C then integral would be the right tool for the job. Note that nowhere in this code do I create a symbolic variable.
A = 1;
B = 2;
C = 3;
f = @(x) A*x.^2+B*x+C; % Added the period to vectorize f
result1 = integral(f, -1, 2)
I suspect you want the expression of the result to contain symbolic variables A, B, and C. If so, use int instead of integral. For this, I do need to create symbolic variables.
syms A B C x
f = A*x^2+B*x+C;
result2 = int(f, x, -1, 2)
We can confirm that result2 gives the same value as result1 when we substitute the values from the first section of code into the symbolic answer.
check = subs(result2, [A B C], [1 2 3])
