how to solve a pde with an integration inside the equation

Hello, My function is

H(x,t) . H(x,0) = 1/2

I need to solve

d/dt(int_1^x dH/dt dx) + dH/dt +2 dH/dx -C(t)/2 = 0

Which method or tool can I use in Matlab? C(t) is not known in advance.

[Satyajeet Sasmal]

You could use the symbolic math toolbox to solve differential equations:

http://www.mathworks.com/help/symbolic/solve-a-single-differential-equation.html