Question

heat of 100g of water when transfer -10C to 150C using this equation q=¡ò_(T_2)^(T_1)¢Æc_p dT

Answer 1

I can't read your equation but I now what you want. There are two equations you need to do this.
The heat transfer WITHIN a phase is
q = mass x specific heat in that phase x (Tfinal-Tinitial).

The second equation you need is for heat transfer AT THE PHASE CHANGE.
q = mass x heat fusion (for solid to liquid) and
q = mass x heat vap (liquid to vapor)

For example. 100 g ice at -10 to zero
q = mass x specific heat x (Tfinal-Tinitial)
q = 100 x specific heat ice x 10 = ?

At the melting point of zero,
q = 100 x heat fusion

For water at zero C to 100 C you have
q = 100 x specific heat liquid H2O x (100)
etc.