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.
$$I_1 = m_1 \frac{x^2}{2} + c_1 x = 17.5\pm??$$
$$I_2 = m_2 \frac{x^2}{2} + c_2 x = 35\pm??$$
$$I_3 = m_3 \frac{x^2}{2} + c_3 x = 52.5\pm??$$
$$BigI = I_1 + I_2 + I_3 = 105\pm??$$
How do I find the error / uncertainty for "BigI"? i.e. Find ?? for "BigI"