\[
\int_{0}^{10} cx \,dx = c\left[\frac{x^2}{2}\right]_{0}^{10} = \frac{c}{2}(10^2 - 0^2) = \frac{c}{2} \times 100=1
\]
$c = \frac{2}{100}$
\[
\int_{1}^{2} \frac{2}{100}x \,dx=\frac{2}{100}\left[\frac{x^2}{2}\right]_{1}^{2} = \left[\frac{x^2}{100}\right]_{1}^{2} = \frac{2^2}{100} - \frac{1^2}{100} = \frac{4 - 1}{100}=\frac{3}{100}
\]
