From original burst, fraction of stellar mass still surviving on Main sequence
When you are calculating fractions, rather than absolute numbers, the value of $\Phi_0$ does not matter, since it will be a multiplying factor in both the numerator and denominator.

You have (almost, see below)  successfully got an expression for the denominator of your fraction.

The numerator is found by calculating an equivalent integral from your lower limit to an upper limit that is instead defined by the most long-lived main sequence stars that are still "alive" - i.e. those with a lifetime equal to the age of our Galaxy.

Finally, you were asked to find the fraction of stellar mass surviving, not the fraction of stars. The stellar mass existing between two mass intervals is
$$M_* = \int_{m_1}^{m_2} m\Phi(m)\ dm$$