Error Propagations for Integrals and Summations

Suppose I have 3 straight lines:

$$y_1 = m_1 x + c_1;$$

$$y_2 = m_2 x + c_2;$$

$$y_3 = m_3 x + c_3;,$$

and

$$m_1 = 1 pm 1.1, c_1 = 1 pm 1.11,$$

$$m_2 = 2 pm 2.2, c_2 = 2 pm 2.22,$$

$$m_3 = 3 pm 3.3, c_3 = 3 pm 3.33.$$

Then integrate $y_1$, $y_2$, $y_3$ w.r.t. $x$ for $x = (0,5)$ and label them as $I_1$, $I_2$, $I_3$ respectively. i.e.

$$I_1 = m_1 frac{x^2}{2} + c_1 x = 17.5pm??$$

$$I_2 = m_2 frac{x^2}{2} + c_2 x = 35pm??$$

$$I_3 = m_3 frac{x^2}{2} + c_3 x = 52.5pm??$$

$$BigI = I_1 + I_2 + I_3 = 105pm??$$

How do I find the error / uncertainty for "BigI"? i.e. Find ?? for "BigI"