$1)$ First verify you can plot the function using the fundamental constants $($Planck$\text{'}$s; Boltzmann's; speed of light in vacuum$)$ and match the graphs posted at a couple of different temperatures.

$2)($a$)$ Next, by integrating to find the area under the curve, calculate the energy $($W$/$m$2)$ emitted by a blackbody at $5777$ K between the wavelengths of $0\mathrm{.}4$m $($micrometer$,$ colloquially known as microns$)$ and $100$m$.$ Express this as a fraction of the total energy emitted by the same body $($Eb $=$T$4).$ Use your code for numerical integration and compare your numbers with Matlab's built$-$in function for integration. $($b$)$ Find the wavelength of peak intensity from your graph and match it with Wien's Law.

$3)($a$)$ Lastly, find the fraction of energy $($as compared to the total$)$ emitted between the wavelengths of $8$ and $14$ um from a blackbody at $289$ K$.$ Find and compare your answers both ways as in #$2$ above $($your own numerical calculation vs Matlab's function$).($b$)$ Find the wavelength of peak intensity from your graph and match it with Wien's Law.