The specific heat of a substance varies with temperature according to c = 0.20 + 0.14T + 0.023T2, with T in °C and c in cal/g·K. Find the energy required to raise the temperature of 2.0 g of this substance from 5.0°C to 15.00°C.

i would have done the integral of the equation using the values 15 and 5. then i would have used the equation Q=delta T x mass x the value i got from the integral

are these steps correct?
thanks

Q = m*intg(c*ΔT) = m*Intg[0.20 + 0.14T + 0.023T2]*dT.
Now find the integration between the limits 5 degrees to 15 degrees.