Calculate heat added for a kmole of ethylene using following equation from $303$ k to $523$ k

Cp$=2\mathrm{.}83+28\mathrm{.}6$ X$10-3$ T$-87\mathrm{.}26$ X$10-7$ T$2$

C$\_$p$^0=12\mathrm{.}184+3\mathrm{.}879$ X $10-3$ T $2\mathrm{.}58$ X $105/$ T$2$

Where Cp is in Kcal$/$kmole k

Solve by analytically and verify your answer with Simson$$s $1/3$ rd rule.