how to solve a pde with an integration inside the equation

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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.

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