Surely you can find the term-wise indefinite integral of a polynomial? So, what is the integral of x? Of x^2? Of x^n, for any value of n?
Next, what is the integral of the polynomial with coefficients [a,b,c]? Still just basic calc here.
In fact, if you have a polynomial of degree n, thus n+1 terms as a vector of coefficients, can you find the integral of each term? Again, basic calculus.
Once you have found the indefinite integral, how do you convert that into a definite integral? Is that not just the difference of two evaluations? Of what? Can you use polyval? Even if not, surely you can figure out how to use Horner's method to evaluate a polynomial? Even if that is a push, a simple loop would suffice.
This is your homework. So you need to make an effort.
