Optimisation of an objective function using integrals

Hello,

I am having some trouble in optimizing an objective function which includes an integral. I've tried the optimization toolbox and 'fmincon' for a constrained nonlinear optimalisation but they don't seem to work when the objective function includes an integral. This is the code of the objective function that I want to maximize and the constraint. Does anyone know how to solve this or what's the best way to maximise this function?

Thanks in advance!

Kind regards

clear all 
close all

syms x A B C
curve = piecewise(0<x<=0.5,         A*x ...
                 ,0.5<x<=1,         B*(x^2) + C  );

Surface = int(curve,0,1);

V0 = 1;
V = x*2*V0;


% Objective function, maximize for A, B and C
Obj_fun= 0.8*int(curve*(V^2),0,1) / (Surface*V0^2);

% Condition
X=int(x*curve,0,1)/Surface <= 0.7;